{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bcc8b28e-8773-478e-9be6-87f9df0f2d77",
   "metadata": {},
   "source": [
    "# Example: Utilizing Predictive and Deterministic with MCMC and SVI\n",
    "\n",
    "In this short tutorial we'll see how to use `deterministic` statements inside a model and inspect its samples with `Predictive` class. Additionally a `GammaPoisson` distribution will be discussed as it'll be used within our model.\n",
    "\n",
    "Check out other tutorials that use `Predictive` and `Deterministic`:\n",
    "\n",
    "- [Example: analyzing baseball stats with MCMC](http://pyro.ai/examples/baseball.html)\n",
    "- [Bayesian Regression - Inference Algorithms (Part 2)](http://pyro.ai/examples/bayesian_regression_ii.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "35e41be6-291e-452d-b934-7e9f3a7532b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.datasets import make_regression\n",
    "import pyro.distributions as dist\n",
    "from pyro.infer import MCMC, NUTS, Predictive\n",
    "from pyro.infer.mcmc.util import summary\n",
    "from pyro.distributions import constraints\n",
    "import pyro\n",
    "import torch\n",
    "\n",
    "pyro.set_rng_seed(101)\n",
    "\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49144812-c5d0-49d8-97fe-b425dda440f2",
   "metadata": {},
   "source": [
    "## Data generation\n",
    "\n",
    "Let's generate our data with `sklearn.datasets.make_regression` method where we can determine the number of features, bias and noise power. Also we'll transform the target variable and make it a `torch` tensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "19fdf2d3-51af-4909-bdc7-876726633a30",
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = make_regression(n_features=1, bias=150., noise=5., random_state=108)\n",
    "\n",
    "X_ = torch.tensor(X, dtype=torch.float)\n",
    "y_ = torch.tensor((y**3)/100000. + 10., dtype=torch.float)\n",
    "y_.round_().clamp_(min=0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f9314d98-59d3-451a-9909-3b1936aef7a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 261,
       "width": 388
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_, y_)\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "407399e5-31df-4fa8-9628-ddb0fd04b038",
   "metadata": {},
   "source": [
    "## Model definition\n",
    "\n",
    "In our model we first sample coefficient from a normal distribution with zero mean and sampled standard deviation. We use `to_event(1)` to move the expanded dimension from `batch_shape` to `event_shape` as we want to sample from a multivariate normal distribution. `deterministic` part is used to register a `name` whose `value` is fully determined by arguments passed to it. Here we use `softplus` to be sure that the resulting `rate` isn't negative. Then we use vectorized version of `plate` to record `counts` from passed dataset as they were sampled from `GammaPoisson` distribution. \n",
    "\n",
    "For now this model might be a little obscure but later we will dive into sampled data to better grasp it's internals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2f987086-f6a7-494c-a37d-5e6ba57e4867",
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(features, counts):\n",
    "    N, P = features.shape\n",
    "    scale = pyro.sample(\"scale\", dist.LogNormal(0, 1))\n",
    "    coef = pyro.sample(\"coef\", dist.Normal(0, scale).expand([P]).to_event(1))\n",
    "    rate = pyro.deterministic(\"rate\", torch.nn.functional.softplus(coef @ features.T))\n",
    "    concentration = pyro.sample(\"concentration\", dist.LogNormal(0, 1))\n",
    "    with pyro.plate(\"bins\", N):\n",
    "        return pyro.sample(\"counts\", dist.GammaPoisson(concentration, rate), obs=counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1985507f-746e-42e4-b059-c14a1dbf05f8",
   "metadata": {},
   "source": [
    "## Inference\n",
    "\n",
    "Inference will be done with MCMC algorithm. IMPORTANT! Please note that only `scale` and `coef` variables are returned in samples dict. `deterministic` parts are available via `Predictive`, similarly as observed samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e295c1a8-eb4e-4f66-8fe7-ca7d4ae1d2de",
   "metadata": {},
   "outputs": [],
   "source": [
    "nuts_kernel = NUTS(model)\n",
    "mcmc = MCMC(nuts_kernel, num_samples=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "41598ceb-09ec-4149-a733-222d0694d2b6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sample: 100%|██████████| 1000/1000 [00:23, 43.11it/s, step size=6.57e-01, acc. prob=0.922]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 22.8 s, sys: 254 ms, total: 23 s\n",
      "Wall time: 23.2 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "mcmc.run(X_, y_);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "134eeb75-3367-4177-9794-11319e1d696e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coef: (500, 1)\n",
      "concentration: (500,)\n",
      "scale: (500,)\n"
     ]
    }
   ],
   "source": [
    "samples = mcmc.get_samples()\n",
    "for k, v in samples.items():\n",
    "    print(f\"{k}: {tuple(v.shape)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e5b9d5c4-aed3-438a-88d1-4d50f249c985",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "counts: (500, 100)\n",
      "rate: (500, 1, 100)\n"
     ]
    }
   ],
   "source": [
    "predictive = Predictive(model, samples)(X_, None)\n",
    "for k, v in predictive.items():\n",
    "    print(f\"{k}: {tuple(v.shape)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "772fa2a1-9336-4931-9f71-e427c96bf51f",
   "metadata": {},
   "source": [
    "After sampling let's see how well our model fits the data. We compute sampled `counts` mean and standard deviation and plot it against the original data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3b6f72cb-8344-4abc-ba6e-b38894377ba9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def prepare_counts_df(predictive):\n",
    "    counts = predictive['counts'].numpy()\n",
    "    counts_mean = counts.mean(axis=0)\n",
    "    counts_std = counts.std(axis=0)\n",
    "    \n",
    "    counts_df = pd.DataFrame({\n",
    "    \"feat\": X_.squeeze(),\n",
    "    \"mean\": counts_mean,\n",
    "    \"high\": counts_mean + counts_std,\n",
    "    \"low\": counts_mean - counts_std,\n",
    "    })\n",
    "\n",
    "    return counts_df.sort_values(by=['feat'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a884c08f-e4ff-4acf-95ab-35d9a0d08646",
   "metadata": {},
   "outputs": [],
   "source": [
    "counts_df = prepare_counts_df(predictive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ca56d0f9-11bd-48c0-8d4a-0162dac03071",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 261,
       "width": 388
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_, y_, c='r')\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x')\n",
    "plt.plot(counts_df['feat'], counts_df['mean'])\n",
    "plt.fill_between(counts_df['feat'], counts_df['high'], counts_df['low'], alpha=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a572f9a-db20-4fa4-af80-a5ac416d4bbe",
   "metadata": {},
   "source": [
    "But where do these values (and uncertainty) come from? Let's find out!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e351f4ac-bb56-4cea-9dad-8db0bd433838",
   "metadata": {},
   "source": [
    "## Inspecting deterministic part\n",
    "\n",
    "Now let's move to the essence of this tutorial. `GammaPoisson` distribution used here and parameterized with (`concentration`, `rate`) arguments is basically an alternative parametrization of `NegativeBinomial` distribution. \n",
    "\n",
    "`NegativeBinomial` answers a question: How many successes will we record before seeing `r` failures (overall) if each trial wins with probability `p`? \n",
    "\n",
    "The reparametrization occurs as follows:\n",
    "\n",
    "- `concentration = r`\n",
    "- `rate = 1 / (p + 1)`\n",
    "\n",
    "First we check sampled mean of `concentration` and `coef` variables..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "eae492b2-3df4-462d-94cd-e60e939b0b49",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Concentration mean:  28.77524757385254\n",
      "Concentration std:  0.7892239689826965\n"
     ]
    }
   ],
   "source": [
    "print('Concentration mean: ', samples['concentration'].mean().item())\n",
    "print('Concentration std: ', samples['concentration'].std().item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "aee98f2b-0201-4de3-abee-f5598757ac43",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coef mean:  -1.2473742961883545\n",
      "Coef std:  0.036095619201660156\n"
     ]
    }
   ],
   "source": [
    "print('Coef mean: ', samples['coef'].mean().item())\n",
    "print('Coef std: ', samples['coef'].std().item())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6fd0556-a81e-4b6f-81eb-dd0877b8aafa",
   "metadata": {},
   "source": [
    "...and do reparametrization (again please note that we get it from `predictive`!)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "00a2edd1-feea-4c8f-b752-5b41a40062e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "rates = predictive['rate'].squeeze()\n",
    "rates_reparam = 1. / (rates + 1.) # here's reparametrization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8b889b8-845f-4929-9e6d-5694cffad010",
   "metadata": {},
   "source": [
    "Now we plot reparametrized `rate`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0f569654-eeca-47e1-9286-ceff6792712f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 277,
       "width": 776
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
    "fig.set_size_inches(13, 4)\n",
    "\n",
    "ax1.scatter(X_, rates_reparam.mean(axis=0))\n",
    "ax1.set_ylabel('mean')\n",
    "ax1.set_xlabel('x')\n",
    "ax1.set_title('rate means')\n",
    "ax2.scatter(X_, rates_reparam.std(axis=0))\n",
    "ax2.set_ylabel('std')\n",
    "ax2.set_xlabel('x')\n",
    "ax2.set_title('rate stds');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5480f4e-cfdc-43f1-8e24-a0edf1268d9b",
   "metadata": {},
   "source": [
    "We see that the probability of success rises with `x`. This means that it will take more and more trials before we observe those 28 failures imposed by `concentration` parameter.\n",
    "\n",
    "Intuitively if we want to record 28 failures where each failure occurs with probability 0.5 then it should also take 28 successes. Let's check if our model follows this logic:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6c70bdcd-e72e-44e8-879f-6f0e69d30c42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 277,
       "width": 779
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
    "fig.set_size_inches(13, 4)\n",
    "\n",
    "ax1.scatter(X_, y_, c='r')\n",
    "ax1.plot(counts_df['feat'], counts_df['mean'])\n",
    "ax1.fill_between(counts_df['feat'], counts_df['high'], counts_df['low'], alpha=0.5)\n",
    "ax1.axhline(samples['concentration'].mean().item(), c='g', linestyle='dashed')\n",
    "ax1.axvline(-0.46, c='g', linestyle='dashed')\n",
    "ax1.set_ylabel('y')\n",
    "ax1.set_xlabel('x')\n",
    "ax1.set_title('fitted model')\n",
    "ax2.scatter(X_, rates_reparam.mean(axis=0))\n",
    "ax2.axhline(0.5, c='g', linestyle='dashed')\n",
    "ax2.axvline(-0.46, c='g', linestyle='dashed')\n",
    "ax2.set_ylabel('mean')\n",
    "ax2.set_xlabel('x')\n",
    "ax2.set_title('rate means');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3a7b0a7-90bb-490b-8cb9-971b9b2a7338",
   "metadata": {},
   "source": [
    "It indeed does. Red lines show that 28 successes and rate 0.5 are located with the same `x` argument. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78066438-2aaa-4706-981f-d77eba71b9d2",
   "metadata": {},
   "source": [
    "## SVI approach\n",
    "\n",
    "`Predictive` class can also be used with the SVI method. In the next section we will use it with `AutoGuide`'s guide and manually designed one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3ea5009f-c82e-4bfb-aab4-2c950eb6f753",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyro.infer import SVI, Trace_ELBO\n",
    "from pyro.optim import Adam\n",
    "from pyro.infer.autoguide import AutoNormal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1dc46d1-cd9b-4b9d-b463-6f50ccfa1cbc",
   "metadata": {},
   "source": [
    "### Manually defined guide\n",
    "\n",
    "First we define our guide with all `sample` sites that are present in the model and parametrize them with learnable parameters. Then we perform gradient descent with `Adam` optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "9a4339a2-c8f3-44e0-a189-82893c27b557",
   "metadata": {},
   "outputs": [],
   "source": [
    "def guide(features, counts):\n",
    "    N, P = features.shape\n",
    "    \n",
    "    scale_param = pyro.param(\"scale_param\", torch.tensor(0.1), constraint=constraints.positive)\n",
    "    loc_param = pyro.param(\"loc_param\", torch.tensor(0.0))\n",
    "    scale = pyro.sample(\"scale\", dist.Delta(scale_param))\n",
    "    coef = pyro.sample(\"coef\", dist.Normal(loc_param, scale).expand([P]).to_event(1))\n",
    "    \n",
    "    concentration_param = pyro.param(\"concentration_param\", torch.tensor(0.1), constraint=constraints.positive)\n",
    "    concentration = pyro.sample(\"concentration\", dist.Delta(concentration_param))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c173a362-acc5-4018-afbe-ebde64ffe273",
   "metadata": {},
   "outputs": [],
   "source": [
    "pyro.clear_param_store()\n",
    "\n",
    "adam_params = {\"lr\": 0.005, \"betas\": (0.90, 0.999)}\n",
    "optimizer = Adam(adam_params)\n",
    "\n",
    "svi = SVI(model, guide, optimizer, loss=Trace_ELBO())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d453e4af-0763-4a46-a8c6-1827d5a4f439",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss:  4509.724546432495\n",
      "Loss:  410.72651755809784\n",
      "Loss:  417.1552972793579\n",
      "Loss:  395.92131960392\n",
      "Loss:  447.41201531887054\n",
      "Loss:  445.11494612693787\n",
      "CPU times: user 21.2 s, sys: 73.4 ms, total: 21.2 s\n",
      "Wall time: 21.3 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "n_steps = 5001\n",
    "\n",
    "for step in range(n_steps):\n",
    "    loss = svi.step(X_, y_)\n",
    "    if step % 1000 == 0:\n",
    "        print('Loss: ', loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fed7b0c-ca4f-4c66-9268-858827f2aee0",
   "metadata": {},
   "source": [
    "`Pyro`s parameter store is comprised of learned parameters that will be used in `Predictive` stage. Instead of providing samples we pass `guide` parameter to construct predictive distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "94acd52c-8e14-4f5e-93a8-1f568bbd6bc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('scale_param', tensor(0.1965, grad_fn=<AddBackward0>)),\n",
       " ('loc_param', tensor(-1.2427, requires_grad=True)),\n",
       " ('concentration_param', tensor(29.1642, grad_fn=<AddBackward0>))]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(pyro.get_param_store().items())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "006799eb-1f80-4981-b8ad-c1643497c384",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale: (500, 1)\n",
      "coef: (500, 1, 1)\n",
      "concentration: (500, 1)\n",
      "counts: (500, 100)\n",
      "rate: (500, 1, 100)\n"
     ]
    }
   ],
   "source": [
    "predictive_svi = Predictive(model, guide=guide, num_samples=500)(X_, None)\n",
    "for k, v in predictive_svi.items():\n",
    "    print(f\"{k}: {tuple(v.shape)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d208a674-22e3-42ae-b59e-986a6fd81434",
   "metadata": {},
   "outputs": [],
   "source": [
    "counts_df = prepare_counts_df(predictive_svi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3f6b8e7d-714d-44c6-b8b2-140b161ed9e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 261,
       "width": 388
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_, y_, c='r')\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x')\n",
    "plt.plot(counts_df['feat'], counts_df['mean'])\n",
    "plt.fill_between(counts_df['feat'], counts_df['high'], counts_df['low'], alpha=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f11cf5f8-d3df-42f4-a191-8c257476c3df",
   "metadata": {},
   "source": [
    "### AutoGuide\n",
    "\n",
    "Another approach for conducting SVI is to rely on automatic guide generation. Here we use `AutoNormal` that underneath uses a normal distribution with a diagonal covariance matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fdfb6fd3-2217-4376-95b4-04ff1c47fbf6",
   "metadata": {},
   "outputs": [],
   "source": [
    "pyro.clear_param_store()\n",
    "\n",
    "adam_params = {\"lr\": 0.005, \"betas\": (0.90, 0.999)}\n",
    "optimizer = Adam(adam_params)\n",
    "\n",
    "auto_guide = AutoNormal(model)\n",
    "\n",
    "svi = SVI(model, auto_guide, optimizer, loss=Trace_ELBO())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "5fe54144-3da1-4d55-b40e-e417b2ae0b46",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss:  3881.8888041973114\n",
      "Loss:  380.9036132991314\n",
      "Loss:  375.7684025168419\n",
      "Loss:  377.94497936964035\n",
      "CPU times: user 18.8 s, sys: 83.8 ms, total: 18.9 s\n",
      "Wall time: 19 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "n_steps = 3001\n",
    "\n",
    "for step in range(n_steps):\n",
    "    loss = svi.step(X_, y_)\n",
    "    if step % 1000 == 0:\n",
    "        print('Loss: ', loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3eccb4d8-e08f-4f03-842a-3e53ecdbd7b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'scale': tensor(1.9367, grad_fn=<ExpandBackward>),\n",
       " 'coef': tensor([-1.2498], grad_fn=<ExpandBackward>),\n",
       " 'concentration': tensor(29.5432, grad_fn=<ExpandBackward>)}"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto_guide(X_, y_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13bb4ff7-060a-4079-8c81-1cd41c511622",
   "metadata": {},
   "source": [
    "As we check `PARAM_STORE` we see that each `sample` site is approximated with a normal distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "dc8f6f2c-4edd-496b-91ce-df0ba9886a20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('AutoNormal.locs.scale',\n",
       "  Parameter containing:\n",
       "  tensor(0.3204, requires_grad=True)),\n",
       " ('AutoNormal.scales.scale', tensor(0.5149, grad_fn=<SoftplusBackward>)),\n",
       " ('AutoNormal.locs.coef',\n",
       "  Parameter containing:\n",
       "  tensor([-1.2510], requires_grad=True)),\n",
       " ('AutoNormal.scales.coef', tensor([0.0413], grad_fn=<SoftplusBackward>)),\n",
       " ('AutoNormal.locs.concentration',\n",
       "  Parameter containing:\n",
       "  tensor(3.3640, requires_grad=True)),\n",
       " ('AutoNormal.scales.concentration',\n",
       "  tensor(0.0299, grad_fn=<SoftplusBackward>))]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(pyro.get_param_store().items())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "211c5936-4d5f-459c-8495-6cb925a66187",
   "metadata": {},
   "source": [
    "Finally we again construct a predictive distribution and plot `counts`. For all three methods we managed to get similar results for our parameters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "bcbdc495-9248-4556-98a6-4281d094f56d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale: (500, 1)\n",
      "coef: (500, 1, 1)\n",
      "concentration: (500, 1)\n",
      "counts: (500, 100)\n",
      "rate: (500, 1, 100)\n"
     ]
    }
   ],
   "source": [
    "predictive_svi = Predictive(model, guide=auto_guide, num_samples=500)(X_, None)\n",
    "for k, v in predictive_svi.items():\n",
    "    print(f\"{k}: {tuple(v.shape)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "1f663b61-a6c6-4d30-bff1-875633b56ada",
   "metadata": {},
   "outputs": [],
   "source": [
    "counts_df = prepare_counts_df(predictive_svi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e3beaa96-a387-4c3c-849f-e6dc2bc6a0d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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c4ULXcNbqD4QicQnacjHD8lQKEkRERERkWWvrGSEQXVCcDec6hwiEnforivJYV1mYtbYWioIEEREREVnWTi/gVKObc3zB8jgFCSIiIiKybPmCYdp6RrJWf+egj64hPwBul2F7ji9YHqcgQURERESWrQtdw4QjNmv1x44ibK4toTDPnbW2FpKCBBERERFZtk5dy14CNX8oHJd7YTksWB6nIEFERERElqXOQR9X+8eyVv+Z60MEw84oRXVxPqvLC7LW1kJTkCAiIiIiy9LRS/1Zq9tay1tXlt+C5XEKEkRERERk2Rn2h+KmAmVaa88IN0YCAHhchm31pVlrazEoSBARERGRZef4lf6sLVi21vJSa+/E+5vXleNdJguWxylIEBEREZFlJRSOxE0FyrSWnhG6o9ueelyGWzZUZq2txaIgQURERESWlbOdQ4wGwlmp21rLyy3xowjFXk9W2lpMChJEREREZNmw1mZ1wXJLzwjdw8t7FAEUJIiIiIjIMnKlb2xiKlCmTR1F2LVMRxFAQYKIiIiILCNHL/dnre6powj7lukoAihIEBEREZFlYmA0SEv3cFbqXkmjCKAgQURERESWiaOX+7DZ2fV0+lqEhuU7igAKEkRERERkGfCHwpy8NpiVuq21vNRyY+L9rnXlFOUv31EEUJAgIiIiIsvAqWuDBEKRrNR9sXuEnuHJ7MrLfRQBFCSIiIiISI6LRCxvZmnBsrWWl1snRxF2r6tY9qMIoCBBRERERHJc640R+keDWal76ijCvoaKrLSz1ChIEBEREZGclq3kaYFQhOcv9Ey8371+ZYwigIIEEREREclh3UN+LveOZqXu5853MzDmjFDke1zs21CRlXaWIgUJIiIiIpKzsrUWoaV7mBMxuyU9sLVmxYwigIIEEREREclRo4EQZzoyv+3paCDET053TbzfXFvC1rrSjLezlClIEBEREZGc9NaVAUKRzGdPe+ZMN2PBMADF+W4e3FaLMSbj7SxlChJEREREJOeEI5bjVwYyXm/PsJ8L3cMT799+Ux0Fee6Mt7PU5VSQYIypNsb8ojHmX4wxF4wxY8aYAWPM88aYXzDGuKZc32iMsbP8fHOWtj5mjHnFGDMcbeNZY8x7sv8pRURERGQu5zqHGPaHMl7vsZg1DhtrimmoLs54G7kg11Zf/BTw10AH8AxwCagDPgj8DfBOY8xPWWunjjsdA76ToL4TiRoxxnwF+AxwBfg6kA98BDhojPl1a+1fzf+jiIiIiEg6rLVZ2fbUFwxz5vrQxPu965d/ZuWZ5FqQcA54L/B9a+1E3m1jzO8BrwAfwgkY/mlKuTettV9MpgFjzN04AcJF4DZrbV/0+J8ArwNfMcZ8z1rbNr+PIiIiIiLp6Bjw0Tnoy3i9J68NTqxxqCnxsqaiIONt5Iqcmm5krX3aWnswNkCIHr8OfC369v55NvPL0dc/HA8Qom20Af8N8AI/P882RERERCRN2RhFiEQsx65M1rt7ffmKW6wcK6eChDmM5+JONDltjTHml4wxvxd93TVLPQ9GX59KcO4HU64RERERkQU06AtyoWt47gtT1NIzwpDPuY0syHOtuC1Pp8q16UYJGWM8wM9F3ya6uX979Ce2zLPAx6y1l2KOFQNrgWFrbUeCes5HX7ck2a/XZzi1LZnyIiIiIhLv2OV+ItOWn2am3nE715TjcS+nZ+mpWy6f/o+BncCT1tofxhwfBb4M3AJURn8O4Cx6vh84FA0MxpVHX2faT2v8eEVGei0iIiIiSQuEIrx1NfPbnnYP+bnSPwaAMbBrXfkcJZa/nB9JMMb8Bs5C4zPAR2PPWWu7gC9MKXLEGPMw8DxwB/CLwF9ko2/W2lsSHY+OMOzLRpsiIiIiy9WZ64P4g5G5L0xR7FqETTUllBbkZbyNXJPTIwnGmE/j3OCfAh6w1vYmU85aG8LZMhVgf8yp8dB0pvBx/Hh/aj0VERERkfnI1ranY8EwZ2O2Pd29viLjbeSinA0SjDG/BXwVJ9fBA9EdjlLRHX2dmG5krR0BrgIlxpjVCcpsjr6eS7EtEREREZmH9huj9I4EMl7vyWsDk9uelnpZU75ytz2NlZNBgjHmPwB/BryJEyB0pVHNndHXlinHn46+PpKgzDunXCMiIiIiC+Do5b65L0pRJGI5fmVyjcOedRUretvTWDkXJBhjPo+zUPl14CFrbc8s1+4zxkz7jMaYh4Dfjr59Ysrp8XwLv2+MqYwp0wj8GuAH/i7tDyAiIiIiKbkx7KetZzTj9cZue1qY52ZLXUnG28hVObVw2RjzMeBLQBh4DviNBNFem7X2sejvfwpsNsa8AFyJHtvFZJ6Dz1trX4gtbK19wRjzp8DvAMeNMd8G8oGfBqqAX1e2ZREREZGF82bM9qTZqnfn2rIVv+1prJwKEoCm6Ksb+K0ZrjkMPBb9/XHgA8BtOFOF8oBO4B+Bv7LWPpeoAmvtZ4wxb+GMHHwKiABvAH9irf3evD+FiIiIiCTFFwxzumMw4/V2D/m5Grvt6dqKjLeRy3IqSLDWfhH4YgrXfwP4RpptPcZksCEiIiIii+DE1QGC4SwkT4vZ9nRzTQklBTl1W5x1GlMRERERkSUpErFZmWo0FghzRtuezkohk4iIiIgsSRe6hycWFmfSiWsDhKPbntaWelmdzW1Pu7ugpRVe+j9QXgoPPQQ7dmSvvQxRkCAiIiIiS461ljfas7/t6e71Wdr2tLUFDh+B9nbn/Uv/B8JB5/f9++ELX3AChiVK041EREREZEmx1vKT0110DPgyXvfFnmGG/THbntZmYdvTo0fh8ScmA4SpjhyBhx+Gv/3bzLedIQoSRERERGTJGA8QTlwdmPviNBy7PFnvzWvLM7/taWsLHDwIdo7F1pEIfPKTcOhQZtvPEAUJIiIiIrIkZDtAiN321GWcICHjDh+ZO0AYF4nAl7+c+T5kgIIEEREREVl02Q4QID552qbaLGx72t018xSjmRw+DCdPZrYfGaAgQUREREQW1UIECGOBMGc7J7c93ZONbU9bWtMrtwSnHClIEBEREZFFsxABAkzf9rS+LAvbnvr96ZUbzHxG6flSkCAiIiIii6a1ZyTrAUJ4yrane7K17anXm165srLM9iMDFCSIiIiIyKI53zWc9TZauuO3Pd1cl4VtTwGam9IrtwTzJShIEBEREZFFEY5YLnZnP0h480r/xO83ryvH48rSLXBNLTQ0pFbmwIElmYFZQYKIiIiILIrLvaP4g5GsttE15ONav5OULWvbnsY6sB8STGUyJNgW1eWCz38+u/1Jk4IEEREREVkUCzHVKDZ52qbaEkq8Gd72dKqmZnj00bhAYfONS3jDofjrXC74+teX5FQjUJAgIiIiIotgIaYajQZC2d/2NJG9e+GjPwuNDbhshLvbj8efP3AAfvQj+MQnFqY/achyKCUiIiIiMt25ziHGAuGstnHi2uDEtqd1ZVna9nQmTc3Q1MxN4QGqzt3lbHNaVuaMHCzBNQhTKUgQERERkQV3LCb7cTaEI5a3Yrc9XZelbU9n4XEZ7rxvDzxy24K2mwkKEkRERERkQV0f8NEx4MtqG8eu9E9se1qU72ZTutuednc5mZT9ficPQnOTs4tREvZsqKC0IC+9dheZggQRERERWVBvZnkUYSwQ5uXW3on3t2yoTH3b09YWOHwE2tunn2tocHYxamqesbg3z8VtjVWptbmEaOGyiIiIiCyY0UCIczGLibPhxZYbBELO1qoVhXnsTnXB8tGj8PgTiQMEcI4//oRz3QxubaiiIM+dWrtLiIIEEREREVkwb10ZmFhMnA09w35OXJ1ci3Df5lW4XSmsRWhtgYMHwc7RR2ud61pbpp0q8XrYu6Ei+TaXIAUJIiIiIrIgwhHL8ZjFxJlmreXI+e6JtGXrqwppWlWcWiWHj8wdIEw2CEeOTDt8R3MVee7cvs3O7d6LiIiISM640DU8sZg4G1p7RrjcOwaAAfZvrkltR6PurpmnGM2krd0pF1VRlMeONVnO6rwAFCSIiIiIyILI5ran4YjlufM9E+93ri1nVYk3tUpaWtNrPKbc3RtTnN60RClIEBEREZGs6xr0cbV/LGv1H7vST/9YEIB8j4u7mqtTr8TvT6/xixehu4vaMi9b0t1qdYnRFqgiIiIiknXZ3PZ0NBCK2/L0jqYqCvPT2FnIm+LIw7jz5+H8ee4tGsb8h99wsirnOI0kiIiIiEhWjQXCnL2evW1PX2rpndzytCiP3esq0quouSntPqwfuM6GH38XHn4Y/vZv065nqVCQICIiIiJZdeLaAKEsbXvaPTTPLU9j1dQ6idLScG/bMQxAJAKf/CQcOpReH5YIBQkiIiIikjWRiM3agmVrLc/FbHm6oaqIpuoUtzyd6sB+SGVHJGDTjcvUD9+YPBCJwJe/PL9+LDIFCSIiIiKSNRe7hxnyZWfb05aeES73Rbc8NbB/86rUtjxNpKkZHn006UDBYLmn/dj0E4cPw8mT8+vLIlKQICIiIiJZk60Fy6FIJG7L05vXllOd6panM9m7Fz76s9A499Sjm69foGpsMPHJHJ5ypN2NRERERCQruof8XOnLzranxy4PMBDd8tTrcXFnUxpbns6mqdn56e6CH//E2cFoinUDnRxoeX3mOgZnCB5ygEYSRERERCQrsrUWYTQQ4pVMbHmajJpa2Lhx+uGRPh49fQSPjcxctqwsO31aAAoSRERERCTjfMEwZ65n50n6ixdvEAg7N+eVRXnsSnfL02RN2Rq13DfM+089S0E4OHu5HM6XoCBBRERERDLu5LUBguHMb3vaPeTn5LXJ4OO+zTXpb3marJitUYuCPj5w8hlKAnNMozpwAHbsyG6/skhBgoiIiIhkVCRiefPywNwXpshay5GYLU8bqoporC7KbCPdXfDyy3DkiPPa3eUcP7Cf/EiY9596lkrfHInhXC74/Ocz268FpoXLIiIiIpJRLT0jDI7NMRUnzXqvxGx5el8mtjwd19oCh49Ae/v0cw0NuO8/wKM/9wh1v/Z/Zq/H5YKvfz2npxqBRhJEREREJE2RiOVq//RpN9lYsDx1y9Ndmdzy9OhRePyJxAECYNrbeOT3f4kN+RH40Y+cqUSJHDjgnP/EJzLTr0WkkQQRERERSUv/WJB/fv0K77x5NZtqSwC4MeznUu9oxtuauuXpHc0Z2vK0tQUOHgQ78/qJ3R3n2dLdDp/8pBMEPPuskyjt0CFnm9OyMmfkIIfXIEylIEFERERE0tI15CMUsXzv+DXetr2OnWvLOXalP+PtjPjjtzy9s7mawrwMbXl6+MisAYLBsufaWedNJAJf/vJkQLCMgoKpFCSIiIiISFq6Bv2Ac4/941OdDIwFOd0xx6LeWN1d0NIKfj94vc5WozW10y57sSV+y9Ob15ZnpP90d804xWhcU++1+IXKhw87owjLOEAABQkiIiIikqauIX/c+9in/bOaY5EwB/Y72Y6ZvuXp/kxuedrSOuclezrOTj946NCyDxJyauGyMabaGPOLxph/McZcMMaMGWMGjDHPG2N+wRiT8PMYY+42xjxpjOmNljlujPktY8yM41TGmPcYY56N1j9sjHnZGPOx7H06ERERkdxhraVryJd6wTkWCdPe7pw/ehRrLYfPdU+caqguonFVcZo9TsDvn/V09egAG/qvTz8xmJ0kcUtJro0k/BTw10AH8AxwCagDPgj8DfBOY8xPWTs5scwY8z7gnwAf8C2gF3gU+DPgnmidcYwxnwa+CtwAngACwIeBx4wxN1trP5utDygiIiKSC/pGg/iDkdQKJbFIGHDOHzzIxbwyrvY7bRjjjCJklHf23ZH2dJwl4ZhFWVlm+7EE5VqQcA54L/B9a+3EX6Ux5veAV4AP4QQM/xQ9XgZ8HQgD91trX4se/zzwNPBhY8xHrLXfjKmrEfgKTjBxq7W2LXr8S8CrwGeMMf9krX0xux9VREREZOnxh8J4XC5+dDLBE/a5zLFIOFYIw3NXR8FTAMDutRVUFeen3uZsmptmPOUNBdjW1Zb4ZI7nQEhGTk03stY+ba09GBsgRI9fB74WfXt/zKkPAzXAN8cDhOj1PuBz0be/MqWZTwBe4K/GA4RomT7gP0ff/vL8PomIiIhI7gmEIvzLG1f5yelOOgZSnGqUxCLhWG+u2cpgNEAo8Li4o7kq9fYSZU6OVVPrrIFI4ObOC+RHQtNPHDiw7NcjQO6NJMxmPK1f7L/mg9HXpxJcfwQYBe42xnittf4kyvxgyjUiIiIiK0I4utVpx4Av9QABklokPG4kr4BX1++ceH9nczUFyW55msKiaMB5//gTcSMc3lCAW6+cnl7e5YLPfz7Zj5HTcmokYSbGGA/wc9G3sTf3W6Ov56aWsdaGgFacQKk5yTIdwAiwzhhTlES/Xk/0A2ybq6yIiIjIUmGt5Ucnr9N+Yx5J0uZYJDzRFnBo0+0EPHkAVBFkZ7JbnqawKHpCUzM8+qiz6CHq9isnKQxN6a/LBV//+oqYagTLJEgA/hjYCTxprf1hzPHxv6iBGcqNH69Io0yGNugVERERWdoudg9z5noK+Q8SmWOR8LjTtU20Vq+beH+gYCy5LU9TXBRNa8vksb174aM/C40NlPpH2N0x5VnxgQNOpuVPfCKpz7Ac5Px0I2PMbwCfAc4AH13k7sSx1t6S6Hh0NGHfAndHREREJGWBUIRnz3bPfeFcZlkkPG7QW8Th5snbp13XzrHhkduSqz+FRdFY66xViJ121NQMTc3cXTBC3tEHnW1Oy8omsyuvMDkdJES3Kv0L4BTwkLV2agaPuZ76jx/vn1JmVfTcjVnKzDTSICIiIrJsvNRygyFfggW8qRpfJDzDVCAL/GTznQQ8zg5G5WND3GtvJMzAPE2Ki6IBaGt3ysXUv6rUy7bbN8N9e1OraxnK2elGxpjfwsllcAJ4ILrD0VTjKfK2JCjvAZpwFjq3JFlmNVAMXLHWzmNSnoiIiMjS1z3k5+il/sxVeGB/3Nz/WMdXb+ZyRT0AxkZ4+PxL5N13b3L1prAoerZy921ahStT2ZxzXE4GCcaY/4CTDO1NnAAhwZ5WgJMLAeCRBOf2A0XACzE7G81V5p1TrhERERFZlqy1PH2mk0iyU3iSkWCRMEBfQSnPN04+vd939Qxr7r8rfjrQbJJcFD1buQ1VRTRUz7kvzYqRc0FCNBHaHwOv40wx6pnl8m8DPcBHjDG3xtRRAPxB9O1fTynzd4Af+HQ0sdp4mUrg96Jvv4aIiIjIMnby2iDX+tPY6nQuMYuEASIYfrzlTkJuZxZ8dXCEO+/b6VyXrCQXRc9W7r7NqzAzjHKsRDm1JsEY8zHgSzgZlJ8DfiPBP2abtfYxAGvtoDHmkzjBwrPGmG/iZFJ+L85Wp98GvhVb2Frbaoz5XeAvgdeMMd8CAjiJ2dYB/1XZlkVERGQ5s9Zy/EoWl19GFwnT3cUbZzroCDhP8F3Aw/dsw1NakFp9SSyKnq3c9tWl1Jal2OYyl1NBAs4aAgA38FszXHMYeGz8jbX2O8aYA8DvAx8CCoALwO8Af2nt9DE0a+1XjTFtwGdx8i+4cBZHf85a+/eZ+CAiIiIiS9XZziE6B7MwijBFT2E5LwUHcZYtw+3NVdSmGiDAnIuiE2psgJpa3C7DXRtXpd7mMpdTQYK19ovAF9Mo92/Au1IscxA4mGpbIiIiIrnMFwxz5FwGtjydw1gwzPeOdxCOPq+tLfVya0NV+hUmyJw8I2Ng/34A9qyvoLwwL/12l6mcW5MgIiIiItnz4sUbjPjDWW0jHLE8+VYHA2NBADwuw8M31SWXNG0mMyyKnsYY57qmZrx5Lm5vmkdgsozl1EiCiIiIiGRP56CPY1f6s97Oscv9XOkbm3j/jh31VJekufg41t69UFHuJEprSzD1qLHBGUGI7pp0e2MVBXnu+be7DClIEBEREREiEcuh011JJy1Olz8U5tW2yfy3dzRVsam2JHMNxCyKpqXV2ebU63UWKcckTist8LBnfUXm2l1mFCSIiIiICMevDizIYuU32vvxhSIAlBV4uK0xS9N9ampnzdZ898ZVeNyaeT8TfTMiIiIiK9yIP8S/XZgt9VTm2jl6uW/i/V3N1fNbh5CmmlIv21eXLni7uURBgoiIiMgKd+RcN4Ho0/1seq2tj2DYmc9UXZzPlvrFuVFX4rS5KUgQERERWcEu3RjlzPWhrLczOBbk+NX+ifd3b6zGtQg36g3VRTRUFy94u7lGQYKIiIjIChUKR3jmbNeCtPVS6w0i0UXRq8sLaFq18DfqxsC9m5Q4LRkKEkRERERWqNfb++gdCWS9nRvDfk53TI5W3L2xelGm+2yrL6O2LI2MzitQxoIEY0xdpuoSERERkewaGA3ySmvv3BdmwIstNyZ+b6guYl1l0YK0G8vtMty1sXrB281VmRxJuGSM+ZYx5sEM1ikiIiIiGWat5ZmzXYQiWU6KAHQMjHGxe2Ti/d2LdKO+Z30F5YV5i9J2LspkkHAO+Cngx8aYc8aYzxhjFK6JiIiILDEXu4dp7RmZ+8J5stbywsXJUYQttSXUli78dJ+CPDe3N2UpH8MylbEgwVp7M3Av8DiwFvgT4Iox5n8aY/Znqh0RERERSV8gFOHZs90L0tal3lGu9I0BzqLhOxdpFOH2pkoK8tyL0nauyujCZWvtC9bajwNrgN8ELgD/F/CMMeaUMeY3jTGVmWxTRERERJL3UssNhnyhrLczdRRhx+oyKovys97uVKUFHnavq1jwdnNdVnY3stYOWGu/GjO68A9AA/CnOKMLjxljbs1G2yIiIiKSWPeQn6OX+hekrQtdw3QN+QFn0fAdTYszirB/Sw0etzb0TJVnAdroAfoAH1AIeIGfAz5qjDkIfMJauzBL60VERERWsFMdg0Rs9hcrRyI2bkejPesqKClI4bazuwtaWsHvB68XmpugpjblftzSUMmWusXJ6pzrshIkGGPygA8BvwTsBwzOwuYvA48Be4D/H/Be4L/hTEkSERERkSwZDYS40jeamcrmuIk/dX2QvtEgAPluF7c0ViZXvrUFDh+B9vbpbTY0wIH90NScVBeba4qVOG0eMhokGGM2AZ8CPg5UAxHgO8B/t9Yeirn0WeBZY8y3gUcy2QcRERERmRSOWI5d6eellhv4g5H5VZbETXxoQyMvt0xOErmloZLC8UXDs5WvrobeGzDTQEd7Ozz+BDz6KOzdO2s3V5Xk88jOelyuhU/YtlxkLEgwxhwC7scZNejAGTX4H9baa7MUex34QKb6ICIiIiKT2npGOHyuOzNZlY8ehYMHYabpStGb+ONv+yDDfi8AhXlu9qyvSK78jRuJj8ey1qmjonzGEYXCfDfv3b0Wr0e7Gc1HJkcSHgCeAf478B1rbTiJMgeB2YIIEREREUnDUyc6ON0xlJnKWlsS3uC3V9QTcOfR1HsVj43gd7l5dRCI5iy7vamKfI9rxvJpsRaOHEkYJLhdhvfsWk15kZKmzVcmg4Tt1tqzqRSw1p4ATmSwDyIiIiIr3og/lLkAAZwpQgkChO/sfBCAMt8wd7Yfp7+wDF+eM4pQVuBh59qyGcvPS1u7s65hymLmB7fVsq6yKHPtrGAZCxJSDRBEREREJDvabmQwm3J3V8I1BOdXbZj4fbCghB9tvTvu/J01eXhcrhnLz1tLa1yQsK+hkp1ryzPfzgqlTWNFRERElpm2ngztYgTOzXgClyvqZyxSPdLP1stnZy0/b37/xK+Nq4q4TzsZZdRC5EkQERERkQUSDEdo783gSELMzfi4AW8xgwUlAOSFg+y9eoaja7cRdDtrAe5pexNX3zW4fBkqK6eVzwivM62puiSfd+5crZ2MMkxBgoiIiMgy8tbVgflvdRorejMe61LMKMKagW7uuvQWuzrOc7F6HWW+ERr7O5yT7e1wKQtTjQCamyjIc/Pe3WsoyNNORpmmIEFERERkmQiGI7zW1jv3halobop7O+bJ5/V1N0283zBwHYDioI9d1y9ML5+NBM+NDbhq63jPrtVUFOVnoQHRmgQRERGRZeL4lQFG/MnsQp+CmlonURrgd3v4zo4HGCgsBcATDrG5+1Jm25uLMbB/Pw9uq2V9lXYyyhYFCSIiIiLLQN9IgBcv9mSn8gP7Cbo9/OuOB+gqrZ44/I5zL1AayOAi6bkYA48+yp4D+7h5nXYyyiZNNxIRERHJceGI5amT1wmGszG3B0IbGjl43wfpCE3eOt7TepRNN66kVpFh9ulHBqiqTpx9ubEB9u+n8badHNhck1q7kjIFCSIiIiI57uXWG1wf8GWl7kjE8uSJ61yOCRDubT3KLVdPp17Z7j3Q3+ckQ5sqGgTQ1OzkVmhpdXZW8nqddRE1tVQVayejhaIgQURERCSHXesf45XWDC5WnnKD/nrJalp7JrdBvWtjNbdQDVfTqLu+Ht73vhmDgAk1tdOyKWsno4WlIEFEREQkR/lDYZ46cR2biVlGrS1w+EhcduTuogpe2vMOcDk35vtW5XN753kIBtJrY3ynpARBwGxcxvCeXaupLNZORgtFQYKIiIhIjjp8tpuBseD8Kzp6FA4eJDbaCBsXP9pyF5FogFA31MM9z/+YtPc0bWxIKTCI9cC2Gu1ktMAUJIiIiIjkkP7RAK09I7TfGKW1JwOZlVtbpgUIAC+v30lPiZMt2R0O8fC5l3ClGyBEty1Nx571FexaV5Feu5I2BQkiIiIiOaJz0Mc/vnqZUCSDuxgdPjItQLheUs1r6ycTpt3TfoyqscH06o9uW0pTc8pFG6qLOLBFOxktBgUJIiIiIjlgxB/i4LFrmQ0Qurvi1iAABF1ufrTlTqxx0mmtHehkz7Wz6dUfu2NRigry3LzrZu1ktFgUJIiIiIgsceGI5fvHOxjyhTJbcUvrtEPPNt9KX5GTqCwvFOTt514ipdv022+HqqrpOxal6NbGSu1ktIgUJIiIiIgscc+e7eJq/1jmK/b7496ermnkVP3GifcHWl+n3J/iuoeqKrjjjnl1qyjfzW6tQ1hUrsXugIiIiIjM7PiVfo5fGchO5V7vxK+9hWU8s+m2ifdbu1q5qbMl9TqnBB7puK2pinyPblMXk759ERERkSXqSt8oz5zpzl4D0bwFQZebJ7fdS9CdB0DF6CAPXnw1tWlG42ICj3SUFnjYtbZ8XnXI/Gm6kYiIiMgSNOgL8v3jHUQykiltBjW10NDA4bw6bhRXAM52p+868zz54TTXP+TPL+HZ7U1VeNx6jr3YFCSIiIiILDHBcISDx64xGghnva0zt9zLya7JQORAy+vUjPanX+HBg87r3r0pFy0vzGPHGo0iLAU5F6YZYz5sjPmqMeY5Y8ygMcYaY56Y4drG6PmZfr45SzsfM8a8YowZNsYMGGOeNca8J3ufTERERASstfzkVCddg/Of2z+XvpEAT3dPBghbutvY2XlxfpVa6wQKramvZ7ijuQq3tjxdEnJxJOFzwG5gGLgCbEuizDHgOwmOn0h0sTHmK8BnovV/HcgHPgIcNMb8urX2r1LvtoiIiMjc3rjUx5nrQ1lvJxSO8OSJDoLRGKFibJAHL7yS3jqEqayFI0dSyo9QVZzP9vqyTLQuGZCLQcJv49y8XwAOAM8kUeZNa+0Xk6ncGHM3ToBwEbjNWtsXPf4nwOvAV4wx37PWtqXedREREZGZtfWM8Nz5ngVp6/D5bnqGAwC4I2HedeZ5vOmuQ0ikrd1J1pZkroQ7m6uVOG0JybkgwVo7ERQYk5U/pF+Ovv7heIAQbbfNGPPfgM8DPw/8x2w0LiIiIitT/2iAJ090kJV1yt1dTuI0vx+8Xs5WreXE1cm8C/tbXqdmpD/z7ba0JhUkrCr1sqWuJPPtS9pyLkhI0xpjzC8B1cAN4EVr7fEZrn0w+vpUgnM/wAkSHkRBgoiIiGSIPxTmu8eu4Q9GMltxawscPgLt7ROH+gpKObTnEfA4251u7m7n5usXMtvuuFlyJtSUetlUW8Irrb3c1VydrYe/kqaVEiS8PfozwRjzLPAxa+2lmGPFwFpg2FrbkaCe89HXLck0aox5fYZTyayjEBERkRXAWstTJ65zIzr1J2OOHnUWEMcMTYSMy8mHEA0QyseGeOjCy5lZh5DIDDkTPC7DIzvrWVXiZWtdKRVFednqgaRpuQcJo8CXcRYtjy+x3wV8EXgAOGSM2WOtHc83Pr7n1kxpDcePV2S6oyIiIrIyvdhyg5bukbkvTMb4tKLr1+HYmzBl6tKR5n30lFQCWVqHMFU0WdtUd29axaoSJ4CoLJ5fXgXJjmUdJFhru4AvTDl8xBjzMPA8cAfwi8BfZKn9WxIdj44w7MtGmyIiIpI7LnQN8XJL7/wrSjCtaKpzqzbw1urJyRD3tb5B7UjfjNfPW2NDwvUI66uK2LehInvtSkbkXJ6ETLDWhoC/ib7dH3NqfKRgpiwe48f7s9AtERERWUG6h/z88GTn/Cs6ehQef2LWAKG7uIJDm26feL+p5xK7Os7PeP28GQP790877M1z8fCOOq0/yAErMkiI6o6+Fo8fiE47ugqUGGNWJyizOfp6Lst9ExERkWVsLBDm4LFrBELzXKjc2jJt3cFUV8pq+fbNbyPgcab1lPqGedv5BOsQMnXfbgw8+mjCHAkPbqulrEDrD3LBSg4S7oy+Tk0H+HT09ZEEZd455RoRERGRlEQiliff6mBgLDj/yg4fmTVAuFC9ju/sfGAiQMgPBXjn2X/DG07Q9u49zhSh+WhsgI/+LOzdO+3U1vpSttaVzq9+WTDLek2CMWYfTiK1yJTjD+EkZQN4YkqxrwEfBX7fGPOdmGRqjcCvAX7g77LZbxEREVm+nrvQw6Xe0flX1N016xSjE3UbeXrTbVjjPBMuCozx/hPPUDPan7hAfT28733RXZG+O23Rc0IGJ7ior3cWKc+QE6G0wMOD22o1zSiH5FyQYIx5P/D+6Nv66OtdxpjHor/3WGs/G/39T4HNxpgXcLI0g7O70XguhM9ba1+Ird9a+4Ix5k+B3wGOG2O+DeQDPw1UAb+ubMsiIiKSjlPXBnmjPUOLhVtaZzz16rqbeKFxz8T78rEhPnDiacr9s+yiNL4T0fgowBzTmCamFSUYNZjq7TfVUZDnnvM6WTpyLkgA9gAfm3KsOfoD0A6MBwmPAx8AbsOZKpQHdAL/CPyVtfa5RA1Yaz9jjHkLZ+TgU0AEeAP4E2vt9zL2SURERGTFuD7g49DpDCxUHjdDorKrZTVxAULtcC/vO/kMRcGZE5uxqjp+FGDvXqgohyNHoC3BaEVjg7MwOcG6g6n2bKigobp4zutkacm5IMFa+0WcPAfJXPsN4BtptvMY8Fg6ZUVERERiDftDHDx2jVAkmTk8SZohUdnRNVsnfl870Mmjpw7PnQvhxg1nEXTsTX9Ts/MznnvB73fanGVa0VTVJfncu2lVUtfK0pJzQYKIiIhILgmFI3z/+DWG/RlOWpYgUdn1kmpaqtdNvH/gwqvJJUuzOKMGiUYGamqTDgpiuYzhkR315LlX8j45uUtBgoiIiEiWWGt55mw31/p9868s0RP9hoaJxcsvr9/JSxtudtYKABv6OqgeG0y+/rZ2p400AoJE7tpYTW1ZQUbqkoWnIEFEREQkSy50DXPi6sDcF85mtmzKdXUAtFWu5qWGXROH3eEQd7UfT72tltaMBAlrKgq4taFy3vXI4lGQICIiIpIFvmCYZ892z33hbI4enX2Xoc5O/O48Dm26Y+LQmoEu3nb+ZSp9Q6m3N8Ni6FTke1w8smM1Lpe2O81lmiQmIiIikgUvXOyZ3zqEJLIpAxxu3sewtwiAwoCPd59+Lr0AAWZcDD2btRWFFOVPbm96YEsN5UXKqpzrNJIgIiIikmEdA2McvzLPaUZzZFMGaK1cw+m6jRPvH7j4KkWheYwGJFgMPZv1VUV8+BZnobQvGGZgLEhtaeqBhiw9ChJEREREMuhy7yhPvtUx1/397ObIpgzgc+dxaNPtE++3dLex+cbl9NtsbEh5PcKudeUTvxfkuZUwbRlRkCAiIiKSAdZaXm/v4/kLPfMLEGDGbMon6jZyuaKe6pE+ukqqGYlOMyoKjHH/xdfSb88YJzlaCkq8HjbWlKTfpixpChJERERE5skfCvOjk51c6BrOUIXTpwy9vH7n5A5GNQ1x5x688AqFoUB6bRkDjz6aVPbkcXluw6O71+DW4uRlS0GCiIiIyDz0DPv53rFr9I0GM1fplAXEr667KW6L01jbulrZ2Hs1vXYaG5wRhBQCBIBHdtZTX64cCMuZggQRERGRNJ29PsRPTncSCEUyW3HMAuLX127jhcY9E+/XDnRSPjZMZ2k15b6h5KcZGWDnTlhVM5mMLc1Mys2rNM1ouVOQICIiIpKicMTy3Plujl7qz04DNbXQ0MDRYAHPN+2bOLyu/zrvO3UYTyScep2Pvhf27p131+7dXK0cCCuAggQRERGRFAz7Qzx5vIOr/WNZbefYnns5cmNyBfTagU7em26A0NiQkQDhvs2ruKWhat71yNKnIEFEREQkSVf7x/j+8WuM+NO4UU/BW1cHeDYmQFg90MV7Tx4mL50AIY2dixK5e2M1tzYqQFgpFCSIiIiIzMFay9HL/Tx3rodIsvubdnc5W5n6/SmtATh5bYCnz3RNvK+PjPG+U8+SH0kje3MaOxclsq2+lNubFCCsJAoSRERERGYRCEX4yelOzl4fSq5Aa4uTLTlRMrSGBjgw825CpzsG+cnpyQChttTL+8eu4w2nESBUVMB75x8gVJfk89D2OozROoSVxLXYHRARERFZqvpGAnzr1UvJBwhHj8LjT8ycLbm93Tl/9Oi0U2euD/LjU50T72tKvXxg71q8BfnpdB3uvHPeAUK+x8W7b15Nvke3jCuN/sVFREREEugfDfDNVy/TM5xkkrLWFjh4kDnTLVvrXNfaMnHofOcQPzrZyXjJVSX5fGDvWgry3HHboaYk3XIxHtpeS3WJd+4LZdlRkCAiIiIyhS8Y5l/fvIYvmMJC4cNH5g4QxlkLR44AcKFrmB+cvD4RIFQXOwFCYZ7bORDdDjUljQ1p5UAY53YZ7t28im31ZWnXIblNQYKIiIhIjEjE8uRbHfSOJDmCAM4i5ZmmGM2krZ2Wi1f5wYmOidiisiiPD+xdS1H+lGWjB/Y7i5CTMc/djFzG8K6b67lNOxmtaAoSRERERGIcPt9N+43R1Aq1tKbcTlvlap5sGyESDRAqivL40L51FHsT7CvT1OzsUjRXoDDP3YyMgXfsrGNTbWla5WX50O5GIiIiIlHHLvfzZjpZlP3+lC5vr6jne9v3E8a56S8vzONDe2cIEMbt3QsV5c40pbYEoxaNDc4IwjwWK79te52mGAmgIEFEREQEgEs3Rnn2bHd6hb3JL+69VF7Hwe37CbucNQdlBR4+uG8tJQVJ3JY1NTs/aeZgmM39W2vYubZ8XnXI8qEgQURERFa83pEA33vrWvKJ0qZKciehK2W1HLzpAGG3cwtWmmf40L51lBXkpdZeTe28g4JY92xaxd4NlRmrT3Kf1iSIiIjIiuYLhvnum1fxByPpV5LEDkRXy2r47o4DhKIBQknIzwdv3UBZYYoBQobd0VSlbMoyjUYSREREJLedPAmHDsHgIJSVwUMPwY4dSV0X3n4T3zveQd9oMP7adKbzHNjvJEpLMBrRUVrNv950P0G3ExAUB0b54MYSKorSTJSWIXs3VHDXxupF7YMsTQoSREREJDcdOgRf+tJEvoE4+/fDF77gBAwzXHe9pJofv/Pf0/O2d04u9m1tcfIdJNrOtKHBCQQSLQweL5cgQLheUsV3djxA0OMECEWBMT5YY6ncsjHlj5xJN68t58CWGkyyW6vKiqIgQURERHLPN74Bn/oURGaYInTkCDz8MPzcz8E//EPcdUGXmxc37OKNtduw13qcp/+PPuqcnC1jcnv75LV7904eP3p0xnJdxZV8Z+eDBDzOiEFhOMAHm4up2rq4AcL21aU8tL1WAYLMSEGCiIiI5JZDh2YPEMZFIvDYY3GHegvL+O72/fQVxmzzaS0c/G709znattYJCCrKnRGF1paEAYIFzq1q4NmNt+KPBggFQT8faCykepEDhM11JTx8U70CBJmVggQRERHJLV/60twBQgJXymo4uH0/Pk+C7UpT2dTIWmekoqk54RSjruJKntl4G9fLVk0c84YCfODE09R0lsG2xQkSKovyuL2pmq31pbhcChBkdgoSREREJHecPJl4DcIczqxq4Edb7iJsMrSxY1s7nD07be3CuVUbnHaiORDAWYPw3lOHqR3pg5E+Z1F0BrcvTUa+x8Wju9dQXZJ8PgdZ2RQkiIiISO44dCilyy3wyrodvNCwO/N9OXYsrp1X193Ei417Jo65I2H2XD3DbVdO4g2HJsu1tC54kPCOHfUKECQlChJEREQkdwwOJn1p2Lg4tPE2TtZlaXqP3zfRztObbuNUTDuVowM8euoIlb6hBOX82enPDO5srmZTbcmCtim5T0GCiIiI5I6ysrmvAXzuPL6/7T4uVdRnry/eAqed7fdxJaaddf3Xeffp5ygIB2cot3BP9DfWlnBnsxKlSeoUJIiIiEjueOihOS8Z8Bbz3ZsO0FNUkdWuDOzYzb8WNtNXVD5xbHvnRR668CpuO8vC6uamrPZrXHVJPu/YUaddjCQtGVq9IyIiIrIAduxwEqXNoLOkim/tfjjrAULHlp1860ZeXIBwV9ubvP38y7MHCI0NWV2PsK6yEICCPDeP7lqD1+Oeo4RIYhpJEBERkdzyhS84idKmbIN6sWotP9h6D0FXdm9vztU08KO6XYSDYcBZoPzwuRfZ0nNp9oLGzBrgzFdtmZcP7VtHS88IXo+LyuL8rLUly59GEkRERCS3PPQQ/I//Aa7J25jz1es5uH1/fIBgDOzZ47xmgAVeWb+DH2y9h3A0NUJhnpsPlvvZcuPy7IWNcTI1NzVnpC9TuYzh7dvrcLkMm2pLWF9VlJV2ZOXQSIKIiIjknl/4BWhshC9/mctHT/ODrfdgiQkGGhucp/ZNzbDrZvje96C3L+3mwsbFoT0PcLq4buJYZVEe7929hoqifKgpdfI3tLVPLxzblyzZ11BBbVlB1uqXlUdBgoiIiOSmhx6i+/Z7Ofjka4TPtzhbi3q9zsLg2Hn/Tc2wew8880zqbTQ34du8je+ziisj4YnD6yoLeffNqynIc0+20dTsJEpraZ25L1lQUZTHnc3VWW1DVh4FCSIiIpKTBsaCfOfoVfxVNXBHzewXp7ntaP+m7XzX1tA3Ormd6U2ry3hwWy1uV4JpTDW1WQ8KygrzGByb7M/btteR59YMcsksBQkiIiKSc8YCYb5z9CrD/tDcF0Na245eK13F9/yVjMXkO7h7YzW3NlQuyraiHpfhbTfVsaWulOfOd3P0Uj871pRp/YFkRc6FncaYDxtjvmqMec4YM2iMscaYJ+Yoc7cx5kljTK8xZswYc9wY81vGmBn3BTPGvMcY86wxZsAYM2yMedkY87HMfyIRERFJRTAc4V/fvErvSCD5QjW10NCQ9OVnahr5511vYyy6QtntMrxzZz23NVYtSoBQWuDh3922nu2ry3C7DPdvreXR3WvYv2WOERSRNOVckAB8Dvg0sAe4OtfFxpj3AUeA/cC/AH8F5AN/BnxzhjKfBg4CO4EngK8Da4DHjDFfmfcnEBERkbSEI5Yn3+qgY8CXeuED++fc6cgCL264mR9uvZuwcW6TCvPcfHDvWrbUlabR4/lbV1nIz9yxgbopC5M31ZZMrokQybBcDBJ+G9gClAG/MtuFxpgynBv8MHC/tfYXrLW/ixNgvAh82BjzkSllGoGvAL3ArdbaX7PW/jawC7gIfMYYc1dGP5GIiIjMqW8kwLdevUxL90h6FTQ1O9uQzhAohFxufrD1Hl7ZcPPEsaqifH76tvWsqShMr8152rOhgg/uW0dRvmaIy8LKub84a+3E1gRJDPd9GKgB/sFa+1pMHT5jzOeAQziBRuyIwicAL/BfrLVtMWX6jDH/GfgG8Ms4QYaIiIik4uRJOHQIBgehrMzJebBjx5zFTncM8vSZLgKhWbIZJ2PvXqgon7Zd6UheAQdv2k9n6aqJYxuqinjXzfWLkrXY7TI8uK2WnWvL575YJAtyLkhI0YPR16cSnDsCjAJ3G2O81lp/EmV+MOUaERERScahQ/ClLzk351Pt3+9kUX7ooWmnAqEIT5/p4nTHYOb6MmW70m5fmO+Gqxi2k8HA7nXl7N9cgyvRDkZZVuL18J7dq1ldvjijFyKw/IOErdHXc1NPWGtDxphWYAfQDJxOokyHMWYEWGeMKbLWjs7WuDHm9RlObUum8yIiIsvCN74Bn/oURGYYBThyBB5+GL7+dfjEJyYOdw36ePKtjrjtRzOqppYWinjq5HWC1lmgbAwc2FzD7vUV2WlzDmsqCnjPrjUUe5f7LZosdcv9L3B8jG5ghvPjxytSLFMcvW7WIEFERGTFO3Ro9gBhXCQCn/wkNDRgH3yQo5f7ef58D+GIzUq3Itbycmsvr7T2ThzLd7t41831NFQXZ6XNudy8tpwHZsq/ILLAlnuQsKistbckOh4dYdi3wN0RERFZeF/60twBwrhIhLE//CN+VL0t/cXJSRj2hXjq5HWu9o9NHCsr8PDe3WuoLkkv6dp8OFua1rBrXcWCty0yk+UeJIyPBsy06mf8eP+UMqui527MUmamkQYREREBZ5FyojUIM7hcVstTw2UMn2rNWtbi1p4Rfnyqk7FgeOLYuspC3rmzflF2ECr2unn3rjWsXaTdk0RmstyDhLPArThbpsatDzDGeIAmIAS0TCmzKlrmxSllVuNMNboy13oEERGRFe/QoaQui2B4acNOXlm/E4uBlswHCZGI5YWWG7ze3jdxzAB3NFVxW1MVrkVIkFZfXsB7dq2mtCBvwdsWmUsu5klIxdPR10cSnNsPFAEvxOxsNFeZd065RkRERGYyOPeORIP5RXz75rfx8vqbnQABwO+fvVCKhn0h/umNK3EBQrHXzQf3reWO5upFCRBuWlPGT92yTgGCLFnLPUj4NtADfMQYc+v4QWNMAfAH0bd/PaXM3wF+4NPRxGrjZSqB34u+/Vq2OiwiIrJslJXNevpC9Tr+5953crWsJv6EN3PrAtpvjPC/XrnEtZgMzQ3VRfzM7RtYV1mUsXaS5TKGB7bV8vBNdXjcy/02THJZzk03Msa8H3h/9G199PUuY8xj0d97rLWfBbDWDhpjPokTLDxrjPkmTibl9+Jsdfpt4Fux9VtrW40xvwv8JfCaMeZbQAAnMds64L9aa5VITUREZC4J8h5YoLu4grfqN3O8fnPics1NiY9H8xrg9zuBRHPTjNOSItbycksvr7RN7l5kgLs2VnNrQ2UyCVkzrjDfzbtvXs36qoUPTkRSlXNBArAH+NiUY83RH4B24LPjJ6y13zHGHAB+H/gQUABcAH4H+Etr7bS91ay1XzXGtEXr+TmcEZdTwOestX+fyQ8jIiKybO3YAfv30/3acS5V1HOlvJarZbX4Pfkzl2lsmH7j39oCh49Ae/v06xsa4MB+Jzla1Ig/xFMnrnMlZvei4nw3j+ysX7DRA2Mg9g6jtszLe3atobxQ04skN+RckGCt/SLwxRTL/BvwrhTLHAQOplJGRERE4r3xG5/jyJ8/xvRHcgkY42RfjnX0KBw8yIwVtLfD40/Ao4/C3r1c7h3lqZPXGQ1M7l60vqqQd9xUv2AJylaXF/Do7jW09ozwensftaVe3nZTHXmaXiQ5JOeCBBEREVn6rLU8d76H18sa4NH3zn6jD06A8OijcSMCtLbMXc5pjMjB7/GqLeWlvvhr71zg3Ys2VBXx6O415Htc7Fxbzo41zrqMxZjeJDIfChJEREQko0LhCD861cnZ60POgb17oaLcyZnQlmDKUGODM4IQGyCAM8UoiSGIUY+XH269m0sxAUJhnjO9aMMCzv/fVFvCO3fWxy1IVnAguUpBgoiIiGSMLxjm4LFrXOkbiz/R1Oz8JLv4uLsr8RqEKbqKK/ne9v0MFRRPHFtXUcgjOxduehHAjjVlvG17HS6XggJZHhQkiIiISEYM+YJ85+hVeoYDM19UU5tcorSW1jkvOV3TyKFNtxN2R29nrOX2fB937Nu0oLkP9jVUsn/zKo0ayLKiIEFERETmraV7mJ+c7mTEH5774mTMklAtbAzPN+7lzbXbJo7lhwI8cvYFmvZsddY3LJC7N1Zze1OVAgRZdhQkiIiISNp8wTBHznVz8trc2ZVTMkNCtdE8L09uu5er5XUTx6pG+nnP6eeo9A2Bd1dm+zGLB7bVsmd9xYK1J7KQFCSIiIhIWtpvjPDjU50M+UKZrzxBQrWWyjU8s+k2hr2T6w829lzi4fMvkR8OzVgu01zG8PCOOravnj2jtEguU5AgIiIiKRkYDfJKWy8nrg5kr5GaWidRWns7g94iDjffQkv1+snz1nJX+zFuu3KKiYk+iRKxZZjHZXjXrtVsrCnJajsii01BgoiIiMDJk3DoEAwOQlkZPPSQkzE5Ruegj9fa+jjfNZRccrR5Cu+/jzeeKeGV9TsIuSdvWQqCft5x7gUa+zomL06UiC3D8j0u3rt7DesXcFtVkcWiIEFERGQlO3QIvvQlJ4fBVPv3Yz//edr23MXr7X1c7h1dsG5d7h3lmU43fY27447vuH6Be9qOURiKWdicKBFbhhXmu/nA3rXUlRVkrQ2RpURBgoiIyEr1jW/Apz4Fkci0U2Hj4syZy7zxH/6cnp++4SREWwAj/hBHzndzrnM47viqwDAPnH6BNUM98QVmSsSWQaUFHj6wdy3VJYkXU4ssRwoSREREVqJDhxIGCH63hxP1mzi6ZhtD+dFpNQcPOhmTs3gjHolYjl3p56WWXgLhyT7lu13c2VzF7nWbcN26NrlEbBlUUZTHB/eto7wwL6vtiCw1ChJERERWoi99KS5AGMov5M01Wzlev5mAe8oNsbXOdKSZgoRksyjP4Fr/GM+c7ZqWhG1LXQn7N9dMZk5ONhFbBuR7XOxZX8G+DZUU5rsXpE2RpURBgoiIyEpz8uTEGoSu4kreWLuNs6saiBjXzGXa2p1gIPYmvbUFDh+B9vbp1zc0wO7dEAjMGDyMBcL828WeaTkWKovyeGBr7aIsEPbmudi7vpK9GyooyFNwICuXggQREZGVYnwHox/+kLaK1by2bjuXy+uTL9/SOnmTf/SoMw1ppm2O2ttnDB7s/vs44V3FCxd68IUmRzM8LsPtTVXs21CJ27WwGYwL893s21DJrnXlCg5EUJAgIiKyvCTayvT69bgdjK6W1vAvu96eet3+6I5CrS2zBwgziGC4OBzhtbe66SqJXwvRvKqYA1tqKFvguf/ePBe3N1axa10F+Z5ZRlJEVhgFCSIiIsvBbFuZAgPeYg7ueScFIT8DBWkmAvN6nSlH3/teSgFCyOXmVG0Tb6zdzkBhady5sgIPB7bW0Lxq4ZOTVRTl8b49a6kqzl/wtkWWOgUJIiIiuW7KVqYWCLo85EdCAARcHr67fT89xZXza+f4cXjqqaQvDxsXb67ZyutrtzOWH59fwB0Jc8vwNW67/3487oV/gr++qoj37FqtqUUiM1CQICIikssSbGV6vbSa1so13H3pLSzwwy13zT9AALh2LelLr5bV8PTG2+gtrog77g0F2NVxjt3XzlEc9MG9Oxdsx6Jxe9ZXsH9LzYKvexDJJQoSREREctmUrUwBjq7ZxqXyem67copX193Eher1C9adMY+X55v2cKpuY9zxEt8I+66dYUfnRfLDockTsYuhs6ysMI+3ba+lobp4QdoTyWUKEkRERHJVdCvTCAYXzhqBofxCzlevJ2JcPLXl7gULECxwqq6Z5xv34subzEycFw5yZ/txdnecw51oHcP4YugsMgb2bqjkruZqLU4WSZKCBBERkRw1+ONneHb7ftYMdnPr1dMAvFW/eSLfwbwDhDVrkppi1FFazXNN++goq4k7vrHnEgda3qA0MDpzYa935nMZsKrUy9u311FfXjD3xSIyQUGCiIjIUpNoG9MdOyZOhyOWo5f6eKnXS7BqHVfLath5/QKeSJjj9Zvn3/6998Kum52pQLMECQPeYl5o3MO5moa446W+Ye6/+BrNfUmsYWhumm9vE3K7DHc0VXFrY5XWHoikQUGCiIjIUjHbNqb798MXvsDVW+7m6dOd9AwHIODM7fd5vLy+7iYqxgYZy8vAk/mSEmedwOkzCU/73Hm8un4Hx9ZsJeya3B3IFQmz9+oZ7rh8grxIeO52Ghuysh5hbUUhD22vpboku6MUIsuZggQREZGlYMo2plONvfAyz//K5zjxi78FFeVw+EhcRuOja7ZS6p9lWk8qxtcJTJkK1FdQyrE1WzhV10zQHZ/0bFPPJe5pe5MK33BybRjjBD4ZlO9xce+mVexaV44xGj0QmQ8FCSIiIvMxx9SgpCTYxnTcgLeYU7XNHFu9xRklOPhd58SUNcBBl4fewrI0P8QU48FBcxMWuFxex5trt9Fauca5uY9RP9jDfa1vsGaoJ/n6jYFHH4Wm5ox012UM21eXcufGasoKFjZjs8hypSBBREQkHUlMDeKhh5KrK8E2pgD9BSV8e+dDDHljtuxMPtFx+pqbCIUjnAl6efP293Ejf/qWodUj/dx++QSbey4RFzZUVTlrGo4fg7b2aeVobHC+nwwECG6XYefaMm5pqKK8UMGBSCYpSBAREUnVHFODOHIEHn4Yvv51+MQnZq8ruo3puJBxcbF6Padqm7hWVkPAvbA3v8PNm3lr0M1bp9sYC4ZhSoDQ1HuVPVfPsH6gk2kTeoyB97zbCQD27oXuLmfxs9/vjE40N2VkDUKe27BzbTm3NFRSqpEDkaxQkCAiIpKKWaYGxYlE4JOfhIaG2UcUDh0CoKu4kpN1GzlT04DPs7ALbsPGxZXyOk7XNnG+tpFIW2/c+TwsN107z+5rZ6n0DSWuJNEUoprajC5Mzve42L2ugn0NFRTl6xZGJJv0vzAREZFUzDA1KKFIBL785RmDhLFAmDMXuzi55510F1dmsJNzC7rctFeu5kL1elqr1hLw5E+7prTAw571FexYXYb3igeOdENbgiAhg1OIEinIc7NnfQV7N1RQkOeeu4CIzJuCBBERkWRNmRqUlMOHnXLRxcyRiOVS7ygnrw1ysXuY8GgBLGCAMOrx8nzTXs6v2kDInfg2YE1FAXvXV9K8qhjXeI6BpmbnJ0tTiBIpynezr6GSXevK8XoUHIgsJAUJIiIiyYpODUqn3ODGLbx1ZYDTHYMM+UKT58pKM9O3OfjdeRxbs4U31mzDnyCXQlmBh421JWyrK6W2bJbsxBmeQpRIaYGHWxoq2bm2nDy3K6ttiUhiChJERESSNTiYdrnDZ7u50JUgh0Bl1fz6lISO0mq+v+0+RrxFccerRgfY1HOZjd4QNf/Xhxc9t0BZYR63N1axfXUpHgUHIotKQYKIiEiyytLLQ+ArLaf9xkjik81N8+jQdKMeLwdvOsCwt4h3nH2BwYJint50e1xm5PKxIQ60vE5T37XJgj3dWR8hmElVcT63NVaxtb4Ut0tJ0ESWAgUJIiIiyZoj78GYx8ux1ZsZzi9i2FvEUH4hI/lFjNXshfAMCQ5qap0dkNoT5BRIw5HmfVwvWwXAv+64P27dQUHQz32tb7Ctqw3X1IQLLa0LHiSsKvVyR1MVm2pKJtc+iMiSoCBBREQkWTt2wK5dcPz4tFMBl4fv7Lif6yXV8ScaG+a++T6wHx5/Auz8MqVdKq/jbO3kyERsgFA90sejp45Q7p9hRMPvn1fbqSgrzOPAlho21hQv+hQnEUlMQYKIiEiyvvENeOstLHChej2D3mI291wC4Meb75weIBgDu3bDyy/PvhtQU7OTY+Dgd5POqOxz53GmtolTdc0E3Hnsb32D5xr3Jrx2Y88lHj73EvmRUMLzgNO3BbBrXTn3bl6l3YpEljgFCSIiIsmIJlG7VlLNc017uVZaA8CRpn0zl6mqgu9+d/rxhgZn9CA2r8DevXDpErz55ozVWaCjdBUn6jdxbtUGwjEjBQdvOjDxe34owJ5rZ2mpWse27jb2XT09PTvyVBleGzFVaYGHt99UR0N18dwXi8iiU5AgIiKShL7//P/w/JZ7uFC9PvlCN24kPt7e7kwvevRRJzgYV1+f8HK/O4/TtU2cqN/EjeKKOZu9a+gKey69xV2X3kqun8lMiUqTx2XYvrqMezevUiI0kRyiIEFERGQmJ08y+uOnebmtj+O+KiLVGdyW01o4eBAqyidHFKY8zR/0FvF8415aqtbGjRqMqxnu5abOFt666XZ6/U4W6NpSL7uaNsGpl5Nb42CMky05g1zGsKG6kK11ZWysLdbUIpEcpCBBREQkRveQn5pXnif45T/g6MVuXl13EwF3Hpgs7NtvrZPBeTxIiO505L9yjRcbdnFszdZpRTzhEFu729h5/QJ1w72Yxga23tHIs2e7GPWHeXB7La6i/Ogah4OzBwrGONfFTnuahzUVBWyrL2NzXQlF+brFEMll+l+wiIiseOGI5ULXMEcv9dHx7Ivc/5df5LU12xluWJP9xtvaobuLvuIKWntGaN18D1fXRbBTgpKa4V52Xr/A1u42vOHoAuToKEBhnpt37lwdX+/evc4oxZEjThtTNTY4IwjzDBDcLsOWulL2baiYPVOziOSUFREkGGPagIYZTndaa6dNAjXG3A18DrgTKATOA38LfNVaG85SV0VEZAH5gmHeujrAscv9DPlC0NoCBw/ybOMsi5EzJILhWlkNrVVraX2rlz47MHkyJkDwBv28+8zzrB/ojK8gmVGApmbnp7vLyYMw2w5LKSrMd7NrXTm71lVQ4l0RtxMiK8pK+l/1APDnCY4PTz1gjHkf8E+AD/gW0As8CvwZcA/wU1nrpYiIZJW1ls5BP6c6Bjh1bZBgbJKznxyad66C2fjcebRXrqG1ai1tlavx50W3HZ2hycbRGzx44gilgbEpJ1IcBaipzdjC5NXlBexaV8GWuhI87ixMwRKRJWElBQn91tovznWRMaYM+DoQBu631r4WPf554Gngw8aYj1hrv5nNzoqISGb1jQQ4c32Is9cH6RsNxp9sbYGf/ASudWSl7atlNby04WaultdOm0Y0zuMybKgqomlVMU2jPRT/23OJszCvWZ2RaUKp8LgMW+tL2b2+gjpNKRJZEVZSkJCsDwM1wD+MBwgA1lqfMeZzwCHgVwAFCSIiS83Jk04+g8FBKCtjeP8DnK1cx9nrQ3QO+hKXOXp07gW+8xA2hie33ctofuG0cyX+EZp6r9E01sv6T/yM82R+rv5c60i8fWoWVBTlsWtdBTvWlGn7UpEVZiUFCV5jzM8CG4AR4DhwJMH6ggejr08lqOMIMArcbYzxWmsXLoe9iIjM7NAh+NKX4MgRxjxeLlav40xNA1f+8SVsQ2N84rLY+fkjw/Dqq0lnOU6FBQYKSji6ZltcgFA3dIOm3qs0915h1Uj/ZJKz3h4YHk4uYEm0fWqGGANNq4rZva6ChuoijJkzDZuILEMrKUioBx6fcqzVGPPz1trDMcfG95s7N7UCa23IGNMK7ACagdOzNWiMeX2GU9uS67KIiMSZMlLAQw8x/MLLXPv9L3G1tIYre95JT3FlfJnxxGV33QlXryWewpMBI3kFXKxeR2dJNTeKK7hRVE5oSm6DPVfPcKD1jcQVtLTC6dPJj2hM3T51HsoK86gt9VJb6mXb6jLKC/PmXaeI5LaVEiT8HfAccBIYwrnB/zTwKeAHxpi7rLXHoteWR18HptUSf7wiO10VEZFpYkYKxh2r38zRv/8xfYVlsOWe2ctbCy+8mLHujOQVcHTtNjpKVxFyewgbw42iCucx/AyMjbC9q3XmSnt7Uw9gotunprIouTDfzb2bVhEIR6gp8VJT6tVUIhGZZkUECdba/zTl0Angl40xw8BngC8CH8hCu7ckOh4dYcj+/noiIsvBN74Bn/oUNhIh6PLg9+RxrayWZzbeimVhpsJYoLOkmraqNbRWrqGrtDqpckWBMapHB6ge6Wdj7xVqR/pmvnhoKL3OtbQmHSTkuQ3v37OW+nItPhaR2a2IIGEWX8MJEmLz0Y+PFJRPvzzueH+W+iQisqL1jwY4fmWA7iE/vhMn8X/tIIFbP4Dfk0ckG1mPZzGSV8Cr63dwbtUGxhIsPI5jLWsHu2i+cZWakV6qRwYoCqWwdK2sNL1O+pNro66sgPs2r1KAICJJWelBQnf0tTjm2FngVmALELemwBjjAZqAENCyEB0UEVkJrLVc7R/j+IsnOHfkNWxnl3OiqxO8xbMXzqBBbzEXqtdRHPAxWFDMq+t2EPRMn59vbIQ1g92sHuxh3UAnBaEApb6R1IKCWI0NUFmVXlmvd9qhmlIvm2pLOHa5n8boImQFByKSipUeJNwZfY294X8a+PfAI8D/nnL9fqAIZ1ck7WwkIjIP1lq6h/ycuT7EueffYOj7T8F4cLCAIhhaq9byVv0m2itXz7iuoDAwRmNfB41912jo68AbDia8LmXGOHkPSkrSK9/cFPd2bUUh792zhoI8N3c0VWl3IhFJy7IPEowx24FL1tqRKccbgb+Kvn0i5tS3gf8CfMQY89WYZGoFwB9Er/nrrHZaRGQZCIUjCTPy9o4EOBub1OzoUTj43axsQzqbQW8RJ+s2cbKumRFv0YzXVY0OcG/rURr7rmV+BYQxTr6D8R2KGhpSW7zc2BC3HqGhuoj37FpDvscVrV4BgoikZ9kHCcBPA58xxhwB2nF2N9oIvBsoAJ4EvjJ+sbV20BjzSZxg4VljzDeBXuC9ONujfhv41oJ+AhGRHGCt5cZIgPYbI7T2jNLRP8a+hkoGx4L4QmE215Zy7Eo/XYMxA7GtLQsWIFigu7iSSxX1tFeu5kp53ay7ERUGfdzZfpyd1y/iykYHGxumZ04+sN/ZrnWWbVBdNkLV6AA1YwPU/PbHqdm3jrJCD26XoSjfeRURma+VECQ8g3Nzvxe4B2f9QT/wPE7ehMetjf+vsbX2O8aYA8DvAx/CCSYuAL8D/OXU60VElq0EeQnYsWPidCAU4XLfKG09I7T2jDDkC8UVf6W11/mlu4u270cTmHm9zhSZmlr44Q+zGiAM5RdyqWI1lyrruVxRz1he4nn5RYExdnReZMf1i9wormA4v5Ct3e2JpxStWQPXriXfCWPg/vudzz3180/V1OyMLMQkVDNYtnW1sX7gOjUjfVSNDuIxwNe/Dh96e/L9EBFJwbIPEqKJ0g7PeeH0cv8GvCvzPRIRyQEJ8hKAcz/f9+A7aP3Vz9DWuJ2r/WOEIwnu8sezGl+/7owWDAxOv6aiHPpnSkmTHp8nn2tlNVyuqKe9op6+opk2qnNs6Otg5/ULNPdewR29KS/3j8xcoLEBPvbx+KzNw8Nw9WriwCHRaMFc9u51vpsjR6g9cZS3X3g5fuvUAwfg8593AjYRkSxZ9kGCiIikKJqXgEgEcAKDtkonP0Br1RoG/SXw53/vPPHeuze+bGsLHD6S3Lz6eQYIFhgoKOFaWQ0dZTVcK11Fb3HFrGUKA2Ns6O9kQ38HG/qvUxIYS77B8QXG4IwCTB0JiA0cZhstmKX66hIvq8sKqL/pLup/5gGq285jnn56xpEcEZFsUZAgIiKTDh2CT32KAC48WFxYjtdv5umNt8VfZ60zJaaifPIp+dGjcdNksiWC4c01W3hj7fZZFxwDuCNh1gSGaMiPsOH4y6wa7ktv8fHUBcaJJAocZlGU76a+vIDV5YWsLi+gtsyL1zMl8/HOnc6PiMgCU5AgIiIAhCOW/v/8J/RWruVsTQNXyurYMHCd89XrExew1pmO1NQcXYCcuQAh4PbQV1DKYEEJAwUlDBaUMFhQzIC3hIHCEuwMSdVckQg1I32sHehkQ1k+a+/eh6dum3NyU43T37YEoxx1dc5rZ+f0c+lMGUqgvDCP5ppiVpcXUl9WQFmhR7sPiciSpSBBRGSFCYYj9I0G6B2J/+lru0rEXw3b7pu49uyqhtkra2t3ptkcPpJ2gGCBnuIKLlSvp6ukit6icgYLkssZkB8KsnqwmzWD3awZ6qZu6AZ5kbBz8ld/Jf7JflOz8zPbtKB5Thmazf1ba2iuSTMXgojIAlOQICKyDIUjloGxIP2jAfpGndf+0SB9owGG/aHE9/MX00wkf/yt1Pb2j+opKuf8qgbOrdpAf1FZSmWLAmPsvH6B2y6fxGMj0y+Ykj8gzmzTglKcMpQsb56LhuqFyxwtIjJfChJERHLcaCDEtf4xrvb76B3x0z8aZHAsRCTVJ/v+NBPJJ5ii43Pn0VlaTZlvhErf0MTx3sIyzq3awPlVG2ZdZGxshMqxIcp9w5T7himb+Bmh3D9Mfjg0Y9m4BcZZtqaigPWVRVjgcu8oHQO+iXOrSvJZW1nI2ooi1lQUKH+BiOQUBQkiIjlmyBfkav8YV/vGuNo/xo3hQGYq9nrTKxfwE3K5uVa6iksVTj6CrpKqiURllaMDVI8O0FdYyo3iyoRV5IWCNPdepbHvKqtG+qkYG0o8QmCYPa9CMguM01BWmEee2+BxufC4DG6XweM2bKsvY2t96cR1XYM+hvwh1pQXUpjvnqVGEZGlTUGCiEgO6Bz0cexyP1f7x+gfTZDgKxOam5K+NIKhq6SKSxV1XK5tomPtXYRdiW+K+4rKE+Yr8IRDNPVeZUtPO419HXjG1xIkkp8HH/mI8/tMi48ztMA4VlVxPge21NC4KrmpQrVlBWR+spKIyMJTkCAisgRFIpZgJELfSJCXW2/Q0j1Lgq9MGR6e8ZQF+grLuFxRz6WKOq6U1xHw5KfchDscorHvGlt6LtHUe3VykfFsjHEChPGb/7kWH89DfXkBm2pLeK2tjzuaq9i9rkLThERkRVKQICKyCLqGfLxw4Qa+YJhgxBIKRwiFncAgFLaJsxhn2w9/NO3QaJ6XV9bv5EL1+jlzElSNDrC+/zrr+6+zbqALawzdxRWEXB6Cbg/54SBrBrtnX08w1UzThzK4wLisMI/t9aVsW11GVbET+OxaVz49Z4GIyAqiIEFEJINC4Qi9IwFujARwuwz5bhfBcAR/KEIwHCEYtowGQrx1ZYBQsoFAMk/Nk32yPuU629TIUGkV/S+9Rr8ppb9pDX2FZfQVluHL8+KfZbSgxD/K+vpy1pd4WP9P/yth9uL1A13JfcZEsjB9CJy4o7Ion7UVhWxbXcraisJp+QoUIIjISqcgQURknjoHffzgrQ5Gg2H8wQSLbdPV2uLkH0i0vWhDAxyI7uAzxzWRxiaGzrcw8PpxBgZH6S8oob+wlP6CQgYG+wi7BoFVsGnVrN3JDwVYP9AZHS3opHJsEPPII7DlDlhdm9Y2qBNuvx2qqjI+fcjjMlSXeKkp9VJb6ryuKvGS70mcjE1ERBwKEkRE5mCt5XLvGC+13mAsEKaqOJ/qknyqi73kuQ0/PNmJL5jE3PpUHD06ewbj9nZ4/PFoB52FxM6NfwkDhaUMFJTQX1DKwMk+Bi+GiBgDtTtJZ1Vt9Ug/d7e9SWNfB66pWwuNb5t6YD88/kT6GZerquCOO9IrG+V2GWpLvdSVF1BXWkBNqZeq4nytKRARSYOCBBGRGfiCYToGfLzSeoNr/ZP73/eOBLgwPosmGwtoW1tmDRCCLjc9xRV0F1c6PyVV9BSVE3an95/0woCPCt8QFWPRH99QNDfBCJ5IaPbFxePbpjY1O2sHDn539i1KZ5LCzkrgBARlBR7qygqoKy9gdXkBNSVePG6NEIiIZIKCBBFZkay1+IIRBn1BBseCzqsvFP09xJAvOPvUoWSmAqU7l/7wkbgAIeDycK6mgSvldXSXVNJXWIo1qd0MFwXGqIhJTuYEBINU+IbxhuexpWrszf3evVBRDv/4j+BLITHbbNmRgTy3YVWJl7oyZ3SgrqxAIwQiIlmmIEFEliVrLSOBMEM+J/vweDAw5Jv8PRhOc2pMslOBtm6Dxsb40YWYkYdQvpdQQwOhylUTuxqFzpwh1D9GqHKNk6CsrIZTdc1JbTda4h+lcmyQ8rEhKnzDlPuGKB9zgoL8SAo7CiUr0c19UzP8u3+X/NQjY/AcOEBDbQmbakooyHMxMBZkLBCmvCjPCQiK8nEpIBARWVAKEkQk51hr8YciDPtDjPhDDPlCDEdfh2KCgaR3D0pFa0tyU2oscOaM8wNQVwsY6Oyku6iCZzfeyrXyKjg1BAzFFCyCm982R92WyrFBaob7qBmJ/gz3URRK4el9Juzfn/j4xNSjmQMpTyRMY38Hm3/9F2j6+bdpNyERkSVGQYKILCnjIwADY0Eu3RiltWeEQV9w4mnyiN8JCAKhDO4ilIrvf39agGCB0bwCAu48eoorOF3bxOWKeoqCPuqHbhByufB5nO1EfRvyGc0vSHm6UMXoIDs7L7BmsIdVI33JJSHLps2bZpxOle9xUf/QPaxuquTovxwicOkKAKX+EVYP9bD5xmUad24k/6tfgIceWshei4hIkhQkiEhWBMMRhn3Rp/v+IKOBMNZCxFqsBYt1duWxREcBghMjAokSiV1NsAf/Quq+1MHZt1oIVGyksHgdBSE/hUE/Y3lejq7ZxlBB8bQyg+4SBgtKZqzT2Aj54RCecAhPJIwn4rzmhcO4I2HyIiEKQgE29VxiQ/91ltSEm7e/feLXgjw3aysLWVtRwNqKImpKvc56gVvWcfsH30bn62/Rd+RFdvp6oKzMCQx27FjEzouIyFwUJIhI2nzBMJd7RycW/Y5P9xn2hRgNLPKT7nmy1hIIR2g73cqxywN0eMugoNbJB5AB6/qv8+DFV6kcG5r74iWmtLqctTdvZE1FIWsrC6kuzp+WjGycx+1i7e27WXv77gXupYiIzIeCBBFJSigcmZj33zca4GL3MJdujBFJd1/8RWKtZSwYZsQfZjQQYsQfZiTgrG0YCYQZ8TsBzogvSGj8o3nL5qw3LxSkKOijIBSgse8aW7rbGfIWMeQtoiAUoCAUwBsMUBDyUxAKLP50oVmMj2oE3HmsH+h0+hsOsmawm3WD3ZQd/BfMzasXu5siIpJFChJEliFrLUP+EMO+EMX5HkoLPLPuDhO7E9BQzIjA5ILgICP+RbypTSIXQThiGQ1Eb/BjbvhHAiFGJwIBJzBIZz2zKxJh041LrB7swZfnxefJZ8zjJeR2s26gi53XL0y78a8aG5zPp84aTyRMmX+EMt9w9HXEefU7uRGKgj6G8wtx2whFwZjF0MbA3/wNvG2OhdUiIpLzFCSI5KjxJ+J9o0H6RgL0jwbpHwvQNxpkYDQQt72nyxjKCj1UFOVRUZhPntvFsH9yitCwL7TkRgQCoQi9R9/ixpmL+H1BvOEAFsNofgGj57oZrahmrGoVo658Rv1BfOluZzoLdzhEmX+Erd3t7Lx+geKgb+5CC82QcKel0sAoZb5hyv0jlB+4h/Lv/jPlo4OU+UcoDoxNX9/gcsFv/za89hocPkzp1DUgBw7A5z+vhcYiIiuEggSRRWatJRxx5r8HQhH8ofjX8ePO72F8wQgDY0H6RgOzJ/uKEbHWCSJGg8Bodj/QVN1dhC62MuYP4ssrwLd6Df7iMnzBML6Q83nGAmHGgmHGAs6T/jF/iKAFKII1N89ctw8gkHKX8j0uivPdFHs9FOd7KPa6KR4eoOjFf6M4MEpxwEdxYIz8cHBpLRaO4YmEKf/Q+yivq6b8//wvyl990UmS5humzDeMx0aiN/Zfdm7sf/oR+PKX4fDh6ZVNDQBOnoRDh2BwUAuNRURWKAUJIvMwvl+/PxTBHwxP/D715t4fCk8cmzgfc02i3XxyQSgSoX80ODHFZzQwOb9/dGCY0aFRRowHv6cqWgBoGQFGMt8ZaykM+iZu8IuDYxQFfBRv3URxc4MTEHg9FOe78bgTbD/62PehO0H25CUgPxykufcq6wc6o4nShii563bMZ/4v54KffXjuG/uHHnJ+kgkAduxQUCAissIpSBDBWZTrD0WiT7edV38wEn3SHf09+uR78vcI/mBkyU3TmVUSc/sTiVgbfcrvBAG9IwEuXe/n6lCQ0GzP2vOK0u6qKxKmwjdM9Ug/xUEffnceYCkK+CgK+ikK+igM+qLvfRQG/bgSzbu5dBw++rNQl3hPf8D5XtoXNkBw2wgNfdfwhoO4I+HoYuHo1qfhMG4bJi8cojgwxob+687IwDiXy3nyHyvZG3sFACIikgQFCbJsTDzVj97cx97k+6I39hOBwMRNvvN7MAvz2RdDJGIZDYYZ9YcY6b6Br6OLglCAYt8wxdcuU3j50sSNtAUCbg+jjRsZ3XcbI9W1caMBo4HwxILfsUB4hgTDyU3GMTZCYdDJK+ANTe7w443u+lMY8FEY8lMUcG72i4K+zE31sRaOHJkx8RfgBE4Z5A0FuOXqaa6U13Gpoh5PJExRcIySgDO6UeofYU/HOSp8w6lX7nLB17+utQEiIpJVChJkSbHWEgxb/KHpN/b+uBv/SMJrcumh/lxiv4vYdQr+UDjuBn7ipt7vzOuPF03klVcFDRswG+6iMOjHEwkzmldAyB39T0BHBDqup9XPMt/4jjhjFAd8FAXGKA46r0XRqT+FIf/izu1va3dGC2YaNfH7Ex+fYtVIHxW+YVw2ggFcNgIWwi4XYZfbWSfgG+aWq6cpCAW4/cpJAm4P+eFZx1viGQM33wzHj08/p8XDIiKyQBQkSFaEwpHJJ/WJpu9MPMWffrOfq/PzY1lrCUXsxOeMXYvgj1mjMHWRcmxAEAhFZnh6P49+GRej+YVplS2IzvcvCjo3/msGutjQf51yfxbWF2RDS+vMQYLXm/Cw20aoHBtkc88ltvRcSnlLUwN4w6HkC4yPEnziE1o8LCIii0pBgswoHJl8oj/1derUnak3/bk8fSdiLcHxG/cpC41nWoDsH/MRGPPjj0AAFzPMjs++8cW70bn6BSE/Po+XkfwCRvIL8eUVxF3uic55L4o++S8uyKNo1w6K8z0U5bsp6umk+F//maKAD7dNbielpchlIxQGxigoyafA48ab56Iwz03B+I93BwV/8bnodCg/BcFANOFZCiMA8zV1lEBrB0REZBEpSFgpok8lO/tH6RsN4seFv7AIX2EJ/l178K1eO2Vqj3Pzu+RNWYgbamwkUFk95cY+EnNjH57h+GQQkH6Ak/n/OeVhyfeP4Q0HyQ8F8YYCeMPBiZv6okA0ILjrdopPn6Cw9eKs4UnYuBjJLyBs3BQFxxJPg7l7G9RUO79//9vgX+AtU2fhiYSj2Yv9E+sZCoJ+vOEgBUFnnUNhyD/x+/j6h/xwCPPTd8FdjYkrbqqCmxqdtQvZNB4I1NdrlEBERJY0BQnL3aFD8KUvTdz8vLb1Hs6taoi/5rvPQkMDHNg/++LOLLDWyQ8QDEXzBIQjBEPxr7Hng+Pbig4NE+wfIBCMEHTnEXAXEfDnET4xCCyNLLfucMi5uS/w4i0pxOtxk+9x4Y3+OL/PfCz/chvuJ/4nSS20+MF3EibUmtYnG6Fsrpv+8Wk5Wdrxx2UjE1l+y33DlPpHnKf24RD5EScYyouEyAs7P+O7/7gjkfmNz8w1j/8LX4CHH4ZICsHxgQPw7nfD97+fOP/Axo1w332wd+/0QEBBgYiILGEKEpazb3wDPvWp5G562tvh8Sfg0UedG5oZjM+1D4SiN+yxN/gxxyZ+H7/hD9sExyLzm5bkLYfEU8nnLd/t3LDnx9y857tjfh8awPv6a+SHAuSHg3hDQfKnPO2fmJ5jjLMFZ9OG1Dpx5LnkAgRIKkBI2vgi3hR2/PGOP8EPBSgM+p3di6K7GY0/3S8M+Cjzj1DqH134yVgHDsx9U/7QQ/A//sfc/5sxBj7yEfj935+s83d/V2sIRERkWVGQsFwdOhR3szOcX8iLG27meP0mrpU5izfDxkXAk0fAnUfQ7SHgziNwsoNgoJRAQVHck/vYm/ylvNrAFQlPTs0JB8lfVUV+SXH8zb7Hhdftnh4ERH/Pc7twmTlmoj/2fbiW5FP2ZLbgnGoR9u2fML6INxosGKwTBAQng4Ci4Bh1w73UD92genRgaa9XSJRTYCa/8AvQ2Jh8ZuJYWkMgIiLLiIKE5epLX4p7GtpRuopPfugLyZUdtjC8cDvW5LkNeW7XxNP7vIlXM+1Y/ssvkdfV6Ty1DwedKSrRV28oEJ9wCqCxAT728cx2OJ0b+Lm24Jxqlqf441NxPJEQ+eGQk4QrHCIvEsYTCeEJhyeucdsIQZcbvyffCQLdefg9eUSMa+KJ//jNf8H4gt0/+V0Kb1pPwUkfhS9/G28osLjbl86krg66umYfbUknp0AqmYlFRESWKQUJy9HJk1ldgOl2xd68O7/neabc5Meej56buNGPuT7PbTBzPbUf190Fp15JrbOp3pwnI93EW9G5/h6XwZvnrD0oiL56Pa6JY16PC+8LXXjPPj+xKNcbCkxMacrqU/sDB+CuPc7vb38AQoHstTUfn/kMfOUrzk18Ok/9k6GRARERWcEUJCxHhw5NO1QU8PG28y/TWVLFcHSffJeNkB/zJN55Oh8iLxwkf9dO8rZtTXBT78LtWqTnyvO8OZ+v8RGPvMAoeSN95EXCzuLaiPPdecJhvGHnZt4bk0144tg7duB98N/jcbvmbqwyD3ouzbvPKZk6LWfHDti/P72A0+WCP/7jmRf0zqeP43kEQE/9RUREskRBwnI0OH13n7VD3fzNP3+Z7yfa3SiRcCNUF2e+b/ORZFbc2J1x8iIh8oLD5FUVRQMd50bf444ZBZkY5TB4XE5AFHvO4zbkuVy4xoOjY9+HN3+Qev/LSyCZAAHSf/rtcqW2O09suUTTctLZ8Sf2Rn6mBb3Xr888AlBeDgMD049rPYCIiMiCUZCwHJWVzb+OGTLQpsrtMnjcBo/L4HY5N99uV+L3HpcLt3vyd0/0XJ7LGb3wHA/iOfUsnuh2mB7rzMX3RMK4bYS8cJC8cHj6zjkffwfcsi4jnwdI/wY+lXLpPMU/cAA++tHkd7SKLTfTzXeyO/7MVleiG/gdO2YfAdDIgIiIyKJSkLAczXIzWjfcy1ieF787n4gx5EXCuCNhZ/Fr9McdCZN3+zbcDZXODXt0ipFn4oY/8fvJG37XRGCQ9HqDZDyyHz57LfVy6d7UzyTdG/hUb3JTeYo/PlXooYdm353n1lvh9tth9erkb77n2vGnsRHe9S741V9N/TPONAKgkQEREZFFZWyy+7BLxhhjXt+3b9++119/PXuNHDiQ/uLlAwfg2Wcz2p2MSfVzZeuzHDqU2g38j36UXrCSTK6LqfP0x2Xjabye8IuIiOSUW265hTfeeOMNa+0tqZTTSMJylc5cckhtT/nFkM7T9WxIdhpOOltwxlpq+/brCb+IiMiKkOQqypXHGLPOGPO3xphrxhi/MabNGPPnxpjKxe5bUsZvYl0p/BPP94Z2IST7uRbis/zCLzgjBAcOJD5/4IBzfuoT/lQ99JAzGnLiBPzFXzgBw1/8hfP+2WeX9r+XiIiI5CSNJCRgjNkIvADUAv8KnAFuB34TeMQYc4+19sYidjE5cz2FjjXfPeUX0nyermfaQm7Bqaf4IiIiskAUJCT233EChN+w1n51/KAx5k+B3wb+EPjlRepbahLdxI5EsykXF+fuvPKltj++buBFRERkGdHC5SmiowgXgDZgo7WT6W2NMaVAB2CAWmvtSJptZH/hsoiIiIiseOkuXNaahOkeiL7+KDZAALDWDgH/BhQBdy50x0REREREFoKmG023Nfp6bobz54GHgS3AodkqMsbMNFSwLb2uiYiIiIhkn0YSpiuPvg7McH78eEX2uyIiIiIisvA0kpBFM839io4w7Fvg7oiIiIiIJEUjCdONjxSUz3B+/Hh/9rsiIiIiIrLwFCRMdzb6umWG85ujrzOtWRARERERyWkKEqZ7Jvr6sDEm7vuJboF6DzAKvLTQHRMRERERWQgKEqaw1l4EfgQ0Ar825fR/AoqBx9PNkSAiIiIistRp4XJivwq8APylMeYh4DRwB04OhXPA7y9i30REREREskojCQlERxNuBR7DCQ4+A2wE/gK401p7Y/F6JyIiIiKSXRpJmIG19jLw84vdDxERERGRhaaRBBERERERiaMgQURERERE4hhr7WL3YcUxxtwoLCys2r59+2J3RURERESWsdOnTzM2NtZrra1OpZyChEVgjGkFyoC2DFa7Lfp6JoN1rkT6HudP3+H86TucP32H86fvcP70Hc6fvsP5awQGrbVNqRRSkLBMGGNeB7DW3rLYfcll+h7nT9/h/Ok7nD99h/On73D+9B3On77DxaM1CSIiIiIiEkdBgoiIiIiIxFGQICIiIiIicRQkiIiIiIhIHAUJIiIiIiISR7sbiYiIiIhIHI0kiIiIiIhIHAUJIiIiIiISR0GCiIiIiIjEUZAgIiIiIiJxFCSIiIiIiEgcBQkiIiIiIhJHQYKIiIiIiMRRkJBjjDGbjTH/wRjztDHmsjEmYIzpNMb8qzHmgTTrvNsY86QxptcYM2aMOW6M+S1jjDvT/V8KjDF5xpjfNMb8nTHmzeh3aI0xv5hGXY3RsjP9fDMbn2GxZfI7jKlzRf0dxsrUZ5/jb/GlbPV/IRhj1hlj/tYYc80Y4zfGtBlj/twYU5liPVXRcm3Req5F612Xrb4vFZn4Do0xz87xd1aQzc+wmIwxHzbGfNUY85wxZjD6eZ9Is66M/D3nokx9j9HvbKa/w+vZ6PtK41nsDkjKvgz8NHAKeBLoBbYC7wXea4z5TWvtXyZbmTHmfcA/AT7gW9H6HgX+DLgH+KmM9n5pKAb+PPp7J3AdWD/POo8B30lw/MQ8612qMvodrtC/QyArn70deCzB8Svp93JxGWM2Ai8AtcC/AmeA24HfBB4xxtxjrb2RRD3V0Xq2AE8D3wS2AT8PvNsYc5e1tiU7n2JxZeo7jPGfZjgemldHl7bPAbuBYZz/PW1Lp5Is/Fvkmox8j1EDTP5/UazhedQp46y1+smhH+DjwN4Exw8AAcAPrE6yrjKgK1rm1pjjBTj/AbPARxb7M2fhO8wH3jn+PQFfjH7WX0yjrsZo2ccW+3Pl8He4Iv8Os/HZo9c/u9ifKwvf0w+jn+3Xpxz/0+jxryVZz/8bvf6/Tjn+G9HjTy32Z82B7/BZ59Zh8T/TInyHDwCbAQPcH/3enlisf4tc/cng99gGtC3251nOP5pulGOstY9Za48mOH4Y5z/e+cDdSVb3YaAG+Ka19rWYunw4kT7Ar8yrw0uQtTZgrf2BtbZjsfuSqzL8Ha7Iv8OolfzZkxJ96vowzg3Bf5ty+j8CI8BHjTHFc9RTAnw0ev0Xp5z+K5wRmHcYY5rn3+ulJVPf4UpnrX3GWnveRu9Q06F/i8x8j7IwNN1oeQlGX5Md7n0w+vpUgnNHgFHgbmOM11rrn2/nlrk1xphfAqqBG8CL1trji9ynXLGS/w6z8dkrjDGfAOpxhuJft9bm8nqE8bVWP7LWRmJPWGuHjDH/hnPTdSdwaJZ67gQKo/UMTaknYoz5IfCpaHvLbcpRpr7DCcaYnwaacEawTwNPL8P/fWZDxv8tVjivMeZngQ04AdZx4Ii1Nry43VoeFCQsE8aYBuAhnJuKI0kW2xp9PTf1hLU2ZIxpBXYAzTj/JyAze3v0Z4Ix5lngY9baS4vSo9yxkv8Os/HZdwPfiD1gjDkGfNRa+9Y8+rpYZvyOos7j3FRtYfabqmTqIVrPcpOp7zDW1E0Zuowxv2at/XYa/VtJsvFvsZLVA49POdZqjPn56AwLmQdNN1oGjDFe4H8CXuCL1tq+JIuWR18HZjg/frwi/d4te6M4i8lvASqjPweAZ3DmWh5azsPGGbKS/w4z/dn/FGexcw1QCtwGfBsncHjaGLM2vW4uqkx9R/o7y8xn/1echfXrcEZmtgF/FC37LWPMI2n3cmVYyX+HmfZ3OA9H63E207gZZ91RI/ADY8zuxeva8qAgYRHMsW1Xop8ZtwaLbpH4OM6NwbeAryzU51hMmfwO58Na22Wt/YK19g1rbX/05wjOk6CXgU1A2tuCZtNS+Q5z3VL6Hq21n7HWvmCt7bHWDltrX7PW/hTO7kmrgM9mq21ZGay1f2at/Z619qq11metPWut/T3gMzj3FH+0yF2UFcJa+5+stU9bazuttaPW2hPW2l/GeVhSyPS1R5IiTTdaHBdxtjtM1rVEB6MBwhM4WyT+I/CzKS4EGn9iUT7D+fHj/SnUuVAy8h1mS3SqyN8AdwD7gb9YyPaTtFS+w1z+O4T5fY8L9dm/BnwI528x12TqO8r1v7P5WIjP/jc42/buMcaUTl33IRNW8t/hQvkaTtCai/+9W1IUJCwCa+1D863DGJOHM8Xop4D/BfxcGgt1zgK34sx9fH1K/R6cRWkhluAivkx8hwugO/q6JKcbLaHvMGf/DmHe3+NCffYl/bc4h7PR15nWCmyOvs40xzvT9eSirH92a63PGDOEM+WyGFCQkNhK/jtcKLn837slRdONcpAxJh/4PzgBwj/gLEhMZyX/09HXRHNI9wNFwAvasSJtd0Zfl+TN7RKykv8OF+qz5/Lf4jPR14eNMXH/n2WMKcWZajkKzLWD00vAGHBPtFxsPS6cKYKx7S0nmfoOZ2SM2YoTIAwBPenWswJk/d9Ccvq/d0uKgoQcE12k/C/A+3B2MPn5qduoJShTbozZZoxZPeXUt3H+Y/4RY8ytMdcXAH8QffvXGet8DpvpOzTG7Jv6H/ro8YeA346+1Vx+9Hc4g5Q/uzGmKPo9bphyfFd0hJGpx4E/jL7Nub9Fa+1F4Ec4ixF/bcrp/4TztPBxa+3I+MHo9xOXxdVaO4yzfquY6XOVPx2t/4d2GWZcztR3aIxpMsZUTa3fGFODs4gUnJwfyznrclKMMXnR73Bj7PF0/i1Wspm+R2PM9kSbghhjGnHynkAO/vduqTHKZZFbjDF/h5N1uQf47ziZCqd61lr7bEyZj+P8B/zvrbUfn1Lf+3FuVHw4W9r1Au/F2abt28C/W44JT4wx/38mU8Hvwdn95QUmt0F83lr7NzHXf5wE36FxtjndHC17JXp4F5P733/eWjt+s7esZOo7jJ57Pyvw7xBS/+zGmPtxnkYettbeH3P8MZxdZ54DLuNkcd6GM0rhBr4O/FIufo/RG4QXgFqc3XVO46z3eQBnWsbd1tobMdc76aetNVPqqY7WswVnFOcVYDvOQ5euaD0Xs/15FkMmvsPo/4a/BjyP85S2F2d/+nfhzKV/DXi7tbY/6x9oEUT/t/r+6Nt64B0438Nz0WM91trPRq9tBFqBdmtt45R6Uvq3WG4y8T0aY76Is+7gCE4ixCFgI/BunIz1TwIfsNYGsvlZlj27BNI+6yf5H5ysynaOny9OKfPx6PHHZqjzHpz/QfXhDMe/hfMU3L3Yn3cRv8fHplyf8DsEfgH4Hk72zGGcG7NLODtN3bfYnzMXvsOV/HeYzmfH2VrX4jwMiD3+fuCfgQvAIE6Sqw7gIPDexf6MGfiO1uMEmR3Rz9YO/DlQmeBa6/zfW8J6qnA2EmiP+Y7+Fli32J9xqX+HOFtMPhb9+7yBk8CzF+fm7teB/MX+jFn+/r44x3/z2mKubZx6LN1/i+X2k4nvEWer8f8NnMFZ5B3EWYvwY+DniD4E18/8fjSSICIiIiIicbQmQURERERE4ihIEBERERGROAoSREREREQkjoIEERERERGJoyBBRERERETiKEgQEREREZE4ChJERERERCSOggQREREREYmjIEFEREREROIoSBARERERkTgKEkREREREJI6CBBERERERiaMgQURERERE4ihIEBERERGROAoSREREREQkjoIEERFZkowx3zHGWGPMbyQ49+XouW8sRt9ERJY7Y61d7D6IiIhMY4ypAo4CdcBd1tqj0eMPAT8CzgC3WWtHF6+XIiLLk4IEERFZsowxdwOHgVZgH1AMvAmU4wQIJxevdyIiy5emG4mIyJJlrX0B+DywGfh/gceBeuA3FCCIiGSPRhJERGRJM8YY4Cng4eih/22t/ZlF7JKIyLKnkQQREVnSrPM0659jDv35InVFRGTF0EiCiIgsacaYzcAbQBBnLcJJ4HZrrW9ROyYisoxpJEFERJYsY4wX+BbOguWfBv4IuBmNJoiIZJWCBBERWcq+AuwF/h9r7Y+B/wj8G/BLxpifWtSeiYgsY5puJCIiS5Ix5gM4axFeBu611oaix9fjbIPqAfZaa1sWrZMiIsuUggQREVlyjDEbcAIBF7DHWts25fz7gO8Ar+IEEIEF7qKIyLKmIEFEREREROJoTYKIiIiIiMRRkCAiIiIiInEUJIiIiIiISBwFCSIiIiIiEkdBgoiIiIiIxFGQICIiIiIicRQkiIiIiIhIHAUJIiIiIiISR0GCiIiIiIjEUZAgIiIiIiJxFCSIiIiIiEgcBQkiIiIiIhJHQYKIiIiIiMRRkCAiIiIiInEUJIiIiIiISBwFCSIiIiIiEkdBgoiIiIiI/H9DAQC4AIHWANJCKwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 261,
       "width": 388
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_, y_, c='r')\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x')\n",
    "plt.plot(counts_df['feat'], counts_df['mean'])\n",
    "plt.fill_between(counts_df['feat'], counts_df['high'], counts_df['low'], alpha=0.5);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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